Theorems on existence and global dynamics for the einstein equations

Living Reviews in Relativity

Volumn 8, Issue , 2005, Pages

  Rendall, Alan D ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27544451664     PISSN: 14338351     EISSN: 14338351     Source Type: Journal    
DOI: 10.12942/lrr-2005-6     Document Type: Review

References (354)

1. Alinhac, S., and Gérard, P., Opérateurs pseudo-différentiels et Théorème de Nash-Moser, Savoirs Actuels, (EDP Sciences, Les Ulis, France, 1991). 2.4
2. Anderson, M.T., "Scalar curvature and geometrization structures for 3-manifolds", in Grove, K., and Peterson, P., eds., Comparison Geometry, vol. 30 of Mathematical Sciences Research Institute Publications, 49-82, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1997). 7.2
3. Anderson, M.T., "On stationary vacuum solutions to the Einstein equations", Ann. Henri Poincare, 1, 977-994, (2000). 3.1
4. Anderson, M.T., "On the structure of solutions to the static vacuum Einstein equations", Ann. Henri Poincare, 1, 995-1042, (2000). 3.1
5. Anderson, M.T., "Asymptotic behavior of future-complete cosmological space-times", Class. Quantum Grow., 21, S11-S28, (2004). 7.2
6. Anderson, M.T., "Existence and stability of even dimensional asymptotically de Sitter spaces", (August, 2004). URL (cited on 17 March 2005): http://arXiv.org/abs/gr-qc/0408072. 5.1
7. Anderson, M.T., and Chruściel, P.T., "Asymptotically simple solutions of the vacuum Einstein equations in even dimensions", (December, 2004). URL (cited on 4 April 2005): http://arXiv.org/abs/gr-qc/0412020. 9.1
8. Andersson, L., "The global existence problem in general relativity", in Chruściel, P.T., and Friedrich, H., eds., The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity, 71-120, (Birkhäuser, Basel, Switzerland; Boston, U.S.A., 2004). 5.3
9. Andersson, L., Chruściel, P.T., and Friedrich, H., "On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations", Commun. Math. Phys., 149, 587-612, (1992). 2.1
10. Andersson, L., and Moncrief, V., "Elliptic-hyperbolic systems and the Einstein equations", Ann. Henri Poincare, 4, 1-34, (2003). 2.3
11. Andersson, L., and Moncrief, V., "Future Complete Vacuum Spacetimes", in Chruściel, P.T., and Friedrich, H., eds., The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity, 299-330, (Birkhäuser, Basel, Switzerland; Boston, U.S.A., 2004). 5.3
12. Andersson, L., Moncrief, V., and Tromba, A., "On the global evolution problem in 2+1 gravity", J. Geom. Phys., 23, 1991-205, (1997). 5.4
13. Andersson, L., and Rendall, A.D., "Quiescent Cosmological Singularities", Commun. Math. Phys., 218, 479-511, (2001). 6.2, 8.1
14. Andersson, L., van Elst, H., Lim, W.C., and Uggla, C., "Asymptotic silence of generic cosmological singularities", Phys. Rev. Lett., 94, 051101, (2005). 8.2, 8.3
15. 1 convergence to equilibrium for the relativistic Boltzmann equation", SIAM J. Math. Anal., 27, 1386-1405, (1996). 4.2
16. Andréasson, H., "Global Foliations of Matter Spacetimes with Gowdy Symmetry", Commun. Math. Phys., 206, 337-365, (1999). 3.6
17. Andréasson, H., "The Einstein-Vlasov System/Kinetic Theory", Living Rev. Relativity, 8, lrr-2005-2, (2005). URL (cited on 22 April 2005): http://www.livingreviews.org/lrr-2005-2. 4.2
18. Andréasson, H., Calogero, S., and Rein, G., "Global classical solutions to the spherically symmetric Nordström-Vlasov system", (August, 2003). URL (cited on 31 March 2005): http://arXiv.org/abs/gr-qc/ 0311027. 4.2
19. Andréasson, H., Rein, G., and Rendall, A.D., "On the Einstein-Vlasov system with hyperbolic symmetry", Math. Proc. Camb. Phil. Soc., 134, 529-549, (2001). Related online version (cited on 28 January 2002): http://arXiv.org/abs/gr-qc/0110089. 3.6
20. 2 symmetric spacetimes with Vlasov matter", Commun. Part. Diff. Eq., 29, 237-262, (2004). 3.6
21. Anguige, K., "A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity", Class. Quantum Grav., 17, 2117-2128, (2000). 6.2
22. Anguige, K., "A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity", Class. Quantum Grav., 17, 2117-2128, (2000). Related online version (cited on 29 January 2002): http://arXiv.org/abs/ gr-qc/0005086. 6.2
23. Anguige, K., "Isotropic Cosmological Singularities. III. The Cauchy Problem for the Inhomogeneous Conformal Einstein-Vlasov Equations", Ann. Phys. (N.Y.), 282, 395-419, (2000). 6.1
24. Anguige, K., and Tod, K.P., "Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes", Ann. Phys. (N.Y.), 276, 257-293, (1999). 6.1
25. Anguige, K., and Tod, K.P., "Isotropic cosmological singularities 2: The Einstein-Vlasov system", Ann. Phys. (N.Y.), 276, 294-320, (1999). 6.1
26. Anninos, P., "Computational Cosmology: From the Early Universe to the Large Scale Structure", Living Rev. Relativity, 4, lrr-2001-2, (2001). URL (cited on 24 January 2002): http://www.livingreviews.org/lrr-2001-2. 7.6
27. 1 trend to equilibrium for the Boltzmann equation", Stud. Appl. Math., 87, 283-288, (1992). 4.2
28. Armendariz-Picon, C., Mukhanov, V., and Steinhardt, P.J., "Essentials of k-essence", Phys. Rev. D, 53, 10351, (2001). 7.5
29. Arnold, V.I., and Ilyashenko, Y.S., "Ordinary differential equations", in Anosov, D.V., and Arnold, V.I., eds., Dynamical Systems I: Ordinary Differential Equations and Smooth Dynamical Systems, vol. 1 of Encyclopaedia of Mathematical Sciences, 1-148, (Springer, Berlin, Germany; New York, U.S.A., 1988). 1
30. Aubin, T., Nonlinear Analysis on Manifolds. Monge-Ampère equations, vol. 252 of Grundlehren der mathematischen Wissenschaften, (Springer, Berlin, Germany; New York, U.S.A., 1982). 2.3
31. Baouendi, M.S., and Goulaouic, C., "Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems", Commun. Part. Diff. Eq., 2, 1151-1162, (1977). 6.2
32. Barnes, A.P., LeFloch, P.G., Schmidt, B.G., and Stewart, J.M., "The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes", Class. Quantum Grav., 21, 5043-5074, (2004). 7.2
33. Barrow, J.D., and Kodama, H., "All universes great and small", Int. J. Mod. Phys. D, 10, 785-790, (2001). 7.1
34. Bartnik, R., "Remarks on cosmological spacetimes and constant mean curvature hypersurfaces", Commun. Math. Phys., 117, 615-624, (1988). 2.1
35. Bartnik, R., "Quasi-spherical metrics and prescribed scalar curvature", J. Differ. Geom., 37, 31-71, (1993). 2.1
36. Bartnik, R., and Fodor, G., "On the restricted validity of the thin sandwich conjecture", Phys. Rev. D, 48, 3596-3599, (1993). 2.1.
37. Bartnik, R., and McKinnon, J., "Particlelike Solutions of the Einstein-Yang-Mills Equations", Phys. Rev. Lett., 61, 141-143, (1988). 3.1
38. Batt, J., Faltenbacher, W., and Horst, E., "Stationary Spherically Symmetric Models in Stellar Dynamics", Arch. Ration. Mech. Anal., 93, 159-183, (1986). 3.1
39. Bauer, S., "Post-Newtonian approximation of the Vlasov- Nordström system", (October, 2004). URL (cited on 13 April 2005): http://arXiv.org/abs/math-ph/0410048. 9.2
40. Bauer, S., and Kunze, M., "The Darwin approximation of the relativistic Vlasov-Maxwell system", (January, 2004). URL (cited on 13 April 2005): http://arXiv.org/abs/math-ph/0401012. 9.2
41. Beale, J.T., Hou, T.Y., and Lowengrub, J.S., "Growth rates for the linearized motion of fluid interfaces away from equilibrium", Commun. Pure Appl. Math., 46, 1269-1301, (1993). 2.6
42. Beig, R., and Schmidt, B.G., "Static, self-gravitating elastic bodies", Proc. R. Soc. London, Ser. A, 459, 109-115, (2002). Related online version (cited on 8 February 2002): http://arXiv.org/abs/gr-qc/0202024. 4.3
43. Beig, R., and Schmidt, B.G., "Relativistic elasticity", Class. Quantum Grav., 20, 889-904, (2003). 2.5
44. Beig, R., and Schmidt, B.G., "Relativistic elastostatics I: bodies in rigid rotation", (November, 2004). URL (cited on 4 April 2004): http://arXiv.org/abs/gr-qc/0411145. 4.3
45. Belinskii, V.A., "Turbulence of a gravitational field near a cosmological singularity", J. Exp. Theor. Phys. Lett., 56, 421-425, (1992). 8.3
46. Belinskii, V.A., Grishchuk, L.P., Zeldovich, Y.B., and Khalatnikov, I.M., "Inflationary stages in cosmological models with a scalar field", Sov. Phys. JETP, 62, 195-203, (1986). 7.4
47. Belinskii, V.A., Khalatnikov, I.M., and Lifshitz, E.M., "Oscillatory approach to a singular point in the relativistic cosmology", Adv. Phys., 19, 525-573, (1970). 3.2
48. Belinskii, V.A., Khalatnikov, I.M., and Lifshitz, E.M., "A general solution of the Einstein equations with a time singularity", Adv. Phys., 31, 639-667, (1982). 3.2
49. Berger, B.K., "Numerical Approaches to Spacetime Singularities", Living Rev. Relativity, 5, lrr-2002-1, (2002). URL (cited on 28 January 2002): http://www.livingreviews.org/lrr-2002-1. 8.2
50. 2 Isometry", Ann. Phys. (N.Y.), 260, 117-148, (1997). 3.6
51. 2-Invariant Cauchy Surfaces", Ann. Phys. (N.Y.), 237, 322-354, (1995). 3.5
52. Berger, B.K., Garfinkle, D., Isenberg, J., Moncrief, V., and Weaver, M., "The singularity in generic gravitational collapse is spacelike, local and oscillatory", Mod. Phys. Lett. A, 13, 1565-1574, (1998). 8.2
53. Berger, B.K., and Moncrief, V., "Exact U(1) symmetric cosmologies with local Mixmaster dynamics", Phys. Rev. D, 62, 023509-1-023509-8, (2000). 8.2
54. Beyer, H., "The spectrum of adiabatic stellar oscillations", J. Math. Phys., 36, 4792-4814, (1995). 4.1
55. Beyer, H., "On the stability of the Kerr metric", Commun. Math. Phys., 221, 659-676, (2001). 3.1
56. Bicak, J., Ledvinka, T., Schmidt, B.G., and Zofka, M., "Static fluid cylinders and their fields: global solutions", Class. Quantum Grav., 21, 1583-1608, (2004). 3.1
57. Bieli, R., "Algebraic expansions for curvature coupled scalar field models", (April, 2005). URL (cited on 28 April 2005): http://arXiv.org/abs/ gr-qc/0504119. 7.5, 7.6
58. Binney, J., and Tremaine, S., Galactic Dynamics, Princeton Series in Astrophysics, (Princeton University Press, Princeton, U.S.A., 1987). 3.1
59. Bizoń, P., "Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere", Commun. Math. Phys., 215, 45-56, (2000). 3.3
60. Bizoń, P., Chmaj, T., and Tabor, Z., "Formation of singularities for equivariant 2+1 dimensional wave maps into 2-sphere", Nonlinearity, 14, 1041-1053, (2001). 3.3
61. Bizoń, P., and Tabor, Z., "On blowup of Yang-Mills fields", Phys. Rev. D, 64, 121701-1-4, (2001). 3.3
62. Bizoń, P., and Wasserman, A.G., "On the existence of self-similar spherically symmetric wave maps coupled to gravity", Class. Quantum Grav., 19, 3309-3322, (2002). Related online version (cited on 5 February 2002): http://arXiv.org/abs/gr-qc/0201046. 3.3
63. Bojowald, M., "Loop quantum cosmology: recent progress", (February, 2004). URL (cited on 21 April 2005): http://arXiv.org/abs/gr-qc/ 0402053. 7.5
64. Börner, G., The Early Universe: Facts and Fiction, Texts and Monographs in Physics, (Springer, Berlin, Germany; New York, U.S.A., 1993), 3rd edition. 7.2
65. Bourguignon, J.-P., "Stabilité par déformation non-linéaire de la métrique de Minkowski (d'après D. Christodoulou et S. Klainerman)", Asterisque, 201-203, 321-358, (1991). 5.2
66. Brauer, U., Singularitäten in relativistischen Materiemodellen, Ph.D. Thesis, (Universität Potsdam, Potsdam, Germany, 1995). 4.1
67. Brauer, U., Rendall, A.D., and Reula, O.A., "The cosmic no-hair theorem and the nonlinear stability of homogeneous Newtonian cosmological models", Class. Quantum Grav., 11, 2283-2296, (1994). 9.3
68. Bressan, A., "The Unique Limit of the Glimm Scheme", Arch. Ration. Mech. Anal., 130, 205-230, (1995). 4.1
69. Bressan, A., Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem, vol. 20 of Oxford Lecture Series in Mathematics and Its Applications, (Oxford University Press, Oxford, U.K.; New York, U.S.A., 2000). 4.1
70. Bressan, A., and Colombo, R.M., "The Semigroup Generated by 2 × 2 Conservation Laws", Arch. Ration. Mech. Anal., 133, 1-75, (1995). 4.1
71. Brodbeck, O., Heusler, M., Straumann, N., and Volkov, M., "Rotating solitons and non-rotating non-static black holes", Phys. Rev. Lett., 79, 4310-4313, (1997). 3.1
72. Burnett, G.A., and Rendall, A.D., "Existence of maximal hypersurfaces in some spherically symmetric spacetimes", Class. Quantum Grav., 13, 111-123, (1996). 3.6
73. Caciotta, G., and Nicolò, F., "Global characteristic problem for Einstein vacuum equations with small initial data: (I) The initial data constraints", J. Hyperbol. Differ. Equations, 2, 201-277, (2005). 9.4
74. Caldwell, R.R., Kamionkowski, M., and Weinberg, N.N., "Phantom energy and cosmic doomsday", Phys. Rev. Lett., 91, 071301, (2003). 7.5
75. Calogero, S., "The Newtonian limit of the relativistic Boltzmann equation", J. Math. Phys., 45, 4042-4052, (2004). 9.2
76. Cantor, M., "A necessary and sufficient condition for York data to specify an asymptotically fiat spacetime", J. Math. Phys., 20, 1741-1744, (1979). 2.1
77. Carr, B.J., Coley, A.A., Goliath, M., Nilsson, U.S., and Uggla, C., "Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions", Phys. Rev. D, 61, 081502-1-5, (2000). 3.3
78. Carr, B.J., Coley, A.A., Goliath, M., Nilsson, U.S., and Uggla, C., "The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models", Class. Quantum Grav., 18, 303-324, (2001). 3.3
79. Cercignani, C., The Boltzmann Equation and Its Applications, vol. 67 of Applied Mathematical Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1994). 4.2
80. Cercignani, C., Illner, R., and Pulvirenti, M., The Mathematical Theory of Dilute Gases, vol. 106 of Applied Mathematical Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1988). 4.2
81. Chae, D., "Global existence of spherically symmetric solutions to the coupled Einstein and nonlinear Klein-Gordon system.", Class. Quantum Grav., 18, 4589-4605, (2001). 3.3
82. Chae, D., "Global existence of solutions to the coupled Einstein and Maxwell-Higgs systems in the spherical symmetry", Ann. Henri Poincare, 4, 35-62, (2003). 3.3
83. Chemin, J.-Y., "Remarques sur l'apparition de singularités dans les écoulements Euleriens compressibles", Commun. Math. Phys., 133, 323-339, (1990). 4.1
84. Chen, J., "Conservation laws for the relativistic p-system", Commun. Part. Diff. Eq., 20, 1605-1646, (1995). 4.1
85. Chen, J., "Conservation Laws for Relativistic Fluid Dynamics", Arch. Ration. Mech. Anal., 139, 377-398, (1997). 4.1
86. Choptuik, M.W., "Universality and Scaling in the Gravitational Collapse of a Massless Scalar Field", Phys. Rev. Lett., 70, 9-12, (1993). 3.3
87. ∞ solutions of hyperbolic nonlinear equations applications to G. R. G.", Gen. Relativ. Gravit., 2, 359-362, (1971). 2.3
88. Choquet-Bruhat, Y., "Future complete Einsteinian spacetimes with U(1) isometry group, the unpolarized case", in Chruściel, P.T., and Friedrich, H., eds., The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity, 251-298, (Birkhäuser, Basel, Switzerland; Boston, U.S.A., 2004). 5.4
89. 1 symmetric solutions of the Einstein-Maxwell-Higgs system", (January, 2005). URL (cited on 1 March 2005): http://arXiv.org/abs/gr-qc/0501052. 5.4
90. Choquet-Bruhat, Y., and Cotsakis, S., "Global hyperbolicity and completeness", J. Geom. Phys., 43, 345-350, (2002). Related online version (cited on 20 February 2002): http://arXiv.org/abs/gr-qc/0201057. 7.2
91. Choquet-Bruhat, Y., and Geroch, R., "Global aspects of the Cauchy problem in general relativity", Commun. Math. Phys., 14, 329-335, (1969). 2.2
92. Choquet-Bruhat, Y., Isenberg, J.A., and Moncrief, V., "Topologically general U(1) symmetric Einstein spacetimes with AVTD behavior", (February, 2005). URL (cited on 13 April 2005): http://arXiv.org/abs/gr-qc/0502104. 6.2
93. Choquet-Bruhat, Y., Isenberg, J.A., and York, J.W., "Einstein constraints on asymptotically Euclidean manifolds", Phys. Rev. D, 61, 084034-1-20, (2000). 2.1
94. Choquet-Bruhat, Y., and Moncrief, V., "Future global in time Einsteinian spacetimes with U(1) isometry group", Ann. Henri Poincare, 2, 1007-1064, (2001). 5.4
95. Choquet-Bruhat, Y., and York, J.W., "The Cauchy problem", in Held, A., ed., General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, vol. 1, 99-172, (Plenum, New York, U.S.A., 1980). 2.1, 2.2
96. Christodoulou, D., "Global existence of generalised solutions of the spherically symmetric Einstein-scalar equations in the large", Commun. Math. Phys., 106, 587-621, (1986). 3.3
97. Christodoulou, D., "The problem of a self-gravitating scalar field", Commun. Math. Phys., 105, 337-361, (1986). 3.3
98. Christodoulou, D., "A mathematical theory of gravitational collapse", Commun. Math. Phys., 109, 613-647, (1987). 3.3, 8.2
99. Christodoulou, D., "The structure and uniqueness of generalised solutions of the spherically symmetric Einstein-scalar equations", Commun. Math. Phys., 109, 591-611, (1987). 3.3
100. Christodoulou, D., "The formation of black holes and singularities in spherically symmetric gravitational collapse", Commun. Pure Appl. Math., 44, 339-373, (1991). 3.3
101. Christodoulou, D., "Bounded variation solutions of the spherically symmetric Einstein-scalar field equations", Commun. Pure Appl. Math., 46, 1131-1220, (1993). 3.3
102. Christodoulou, D., "Examples of naked singularity formation in the gravitational collapse of a scalar field", Ann. Math., 140, 607-653, (1994). 3.3
103. Christodoulou, D., "Self-Gravitating Fluids: A Two-Phase Model", Arch. Ration. Mech. Anal., 130, 343-400, (1995). 3.3
104. Christodoulou, D., "Self-Gravitating Fluids: The Continuation and Termination of a Free Phase Boundary", Arch. Ration. Mech. Anal., 133, 333-398, (1996). 3.3
105. Christodoulou, D., "Self-Gravitating Fluids: The Formation of a Free Phase Boundary in the Phase Transition from Soft to Hard", Arch. Ration. Mech. Anal., 134, 97-154, (1996). 3.3
106. Christodoulou, D., "The instability of naked singularities in the gravitational collapse of a scalar field", Ann. Math. (2), 149, 183-217, (1999). 3.3
107. Christodoulou, D., and Klainerman, S., "Asymptotic properties of linear field equations in Minkowski space", Commun. Pure Appl. Math., 43, 137-199, (1990). 5.2
108. Christodoulou, D., and Klainerman, S., The global nonlinear stability of the Minkowski space, vol. 41 of Princeton Mathematical Series, (Princeton University Press, Princeton, U.S.A., 1993). 5.2
109. Christodoulou, D., and Lindblad, H., "On the motion of the free surface of a liquid", Commun. Pure Appl. Math., 53, 1536-1602, (2000). 2.6
110. Christodoulou, D., and Ó Murchadha, N., "The boost problem in general relativity", Commun. Math. Phys., 80, 271-300, (1981). 2.1, 2.2
111. Christodoulou, D., and Tahvildar-Zadeh, A.S., "On the asymptotic behaviour of spherically symmetric wave maps", Duke Math. J., 71, 31-69, (1993). 3.5
112. Christodoulou, D., and Tahvildar-Zadeh, A.S., "On the regularity of spherically symmetric wave maps", Commun. Pure Appl. Math., 46, 1041-1091, (1993). 3.5
113. Chruściel, P.T., "On Space-Time with U(1) × U(1) Symmetric Compact Cauchy Surfaces", Ann. Phys. (N.Y.), 202, 100-150, (1990). 3.6
114. Chruściel, P.T., On Uniqueness in the Large of Solutions of Einstein's Equations (Strong Cosmic Censorship), vol. 27 of Proceedings of the Centre for Mathematics and its Applications, (Australian National University Press, Canberra, Australia, 1991). 1.
115. Chruściel, P.T., "Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation", Commun. Math. Phys., 137, 289-313, (1991). 9.4
116. Chruściel, P.T., Isenberg, J.A., and Moncrief, V., "Strong cosmic censorship in polarised Gowdy spacetimes", Class. Quantum Grav., 7, 1671-1680, (1990). 1.6
117. Chruściel, P.T., Isenberg, J.A., and Pollack, D., "Gluing initial data sets for general relativity", Phys. Rev. Lett., 93, 081101, (2004). 2.1
118. Claudel, C.M., and Newman, K.P., "The Cauchy problem for quasi-linear hyperbolic evolution problems with a singularity in the time", Proc. R. Soc. London, Ser. A, 454, 1073-1107, (1998). 6.1
119. Coley, A.A., and van den Hoogen, R.J., "The dynamics of multi-scalar field cosmological models and assisted inflation", Phys. Rev. D, 62, 023517, (2000). 7.5
120. Coley, A.A., and Wainwright, J., "Qualitative analysis of two-fluid Bianchi cosmologies", Class. Quantum Grav., 9, 651-665, (1992). 7.1
121. Corvino, J., "Scalar curvature deformation and a gluing construction for the Einstein constraint equations", Commun. Math. Phys., 214, 137-189, (2000). 2.1
122. Dafermos, M., "Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations", Ann. Math., 158, 875-928, (2003). 3.4
123. Dafermos, M., "On naked singularities and the collapse of self-gravitating Higgs fields", (March, 2004). URL (cited on 4 April 2005): http://arXiv.org/abs/gr-qc/0403033. 3.3
124. Dafermos, M., "Spherically symmetric spacetimes with a trapped surface", (March, 2004). URL (cited on 31 March 2005): http://arXiv.org/ abs/gr-qc/0403032. 3.3
125. Dafermos, M., and Rendall, A.D., "An extension principle for the Einstein-Vlasov system in spherical symmetry", (November, 2004). URL (cited on 1 April 2005): http://arXiv.org/abs/gr-qc/0411075. 3.3
126. Dafermos, M., and Rodnianski, I., "A proof of Price's law for the collapse of a self-gravitating scalar field", (September, 2003). URL (cited on 31 March 2005): http://arXiv.org/abs/gr-qc/0309115. 3.4
127. Dain, S., "Trapped surfaces as boundaries for the constraint equations", Class. Quantum Grav., 21, 555-574, (2004). 2.1
128. Dain, S., and Nagy, G., "Initial data for fluid bodies in general relativity", Phys. Rev. D, 65, 084020-1-15, (2002). Related online version (cited on 30 January 2002): http://arXiv.org/abs/gr-qc/0201091. 2.6
129. Damour, T., "Cosmological singularities, Einstein billiards and Lorentzian Kac-Moody algebras", (January, 2005). URL (cited on 28 July 2005): http://arXiv.org/abs/gr-qc/0501064. 8.2
130. Damour, T., Henneaux, M., Rendall, A.D., and Weaver, M., "Kasner-like behaviour for subcritical Einstein-matter systems", Ann. Henri Poincare, 3, 1049-1111, (2002). URL (cited on 20 February 2002): http://arXiv.org/abs/gr-qc/0202069. 6.2
131. de Oliveira, H.P., Ozorio de Almeida, A.M., Damião Soares, I., and Tonini, E.V., "Homoclinic chaos in the dynamics of a general Bianchi type-IX model", Phys. Rev. D, 65, 083511-1-9, (2002). Related online version (cited on 17 February 2002): http://arXiv.org/abs/gr-qc/0202047. 7.3
132. DiPerna, R.J., and Lions, P.-L., "On the Cauchy problem for Boltzmann equations: Global existence and weak stability", Ann. Math., 130, 321-366, (1989). 4.2
133. Dossa, M., "Espaces de Sobolev non isotropes, à poids et problèmes de Cauchy quasi-linéaires sur un conoïde caractéristique", Ann. Inst. Henri Poincare A, 66, 37-107, (1997). 9.4
134. Dudyński, M., and Ekiel-Jezewska, M.L., "Global existence proof for thé relativistic Boltzmann equation", J. Stat. Phys., 66, 991-1001, (1992). 4.2
135. 3+1", Commun. Math. Phys., 83, 171-212, (1982). 2.3, 3.3
136. Ehlers, J., "The Newtonian limit of general relativity", in Ferrarese, G., ed., Classical Mechanics and Relativity: Relationship and Consistency, International Conference in Memory of Carlo Cattaneo, Elba 9-13 July 1989, Monographs and Textbooks in Physical Science, (Bibliopolis, Naples, Italy, 1991). 9.2
137. Evans, L.C., Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, (American Mathematical Society, Providence, U.S.A., 1998). 1.
138. Felder, G., Kofman, L., and Starobinsky, A.A., "Caustics in tachyon matter and other Born-Infeld scalars", J. High Energy Phys., 0209, 026, (2001). 7.5
139. Fischer, A., and Moncrief, V., "The Einstein flow, the σ-constant and the geometriztion of 3-manifolds", Class. Quantum Grav., 16, L79-L87, (1999). 7.2
140. Fjällborg, M., "On the cylindrically symmetric Einstein-Vlasov system", (March, 2005). URL (cited on 31 March 2005): http://arXiv.org/abs/ gr-qc/0503098. 3.5
141. Friedrich, H., "Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant", J. Geom. Phys., 3, 101-117, (1986). 5.1, 7.6
142. Friedrich, H., "On the global existence and asymptotic behaviour of solutions to the Einstein-Yang-Mills equations", J. Differ. Geom., 34, 275-345, (1991). 9.1
143. Friedrich, H., "Einstein equations and conformal structure: Existence of anti-de Sitter-type spacetimes", J. Geom. Phys., 17, 125-184, (1995). 5.1
144. Friedrich, H., "Hyperbolic reductions of Einstein's field equations", Class. Quantum Grav., 13, 1451-1469, (1996). 2.2
145. Friedrich, H., "Evolution equations for gravitating ideal fluid bodies in general relativity", Phys. Rev. D, 57, 2317-2322, (1998). 2.6
146. Friedrich, H., "Gravitational fields near spacelike and null infinity", J. Geom. Phys., 24, 83-172, (1998). 5.1, 9.1
147. Friedrich, H., and Nagy, G., "The initial boundary value problem for Einstein's vacuum field equations", Commun. Math. Phys., 201, 619-655, (1999). 9.5
148. Friedrich, H., and Rendall, A.D., "The Cauchy problem for the Einstein equations", in Schmidt, B.G., ed., Einstein's Field Equations and Their Physical Implications: Selected Essays in Honour of Jürgen Ehlers, vol. 540 of Lecture Notes in Physics, (Springer, Berlin, Germany; New York, U.S.A., 2000). 2, 2.2, 2.0
149. Fritelli, S., and Reula, O.A., "On the Newtonian limit of general relativity", Commun. Math. Phys., 166, 221-235, (1994). 9.2
150. Garfinkle, D., "Numerical simulations of generic singuarities", Phys. Rev. Lett., 93, 124017, (2004). 8.2
151. Gibbons, G.W., "Phantom matter and the cosmological constant", (February, 2003). URL (cited on 21 April 2005): http://arXiv.org/abs/gr-qc/ 0302199. 7.5
152. Gibbons, G.W., "Thoughts on tachyon cosmology", Class. Quantum Grav., 20, S321-S346, (2003). 7.5
153. Glassey, R.T., and Schaeffer, J., "The 'two and one half dimensional' relativistic Vlasov-Maxwell system", Commun. Math. Phys., 185, 257-284, (1997). 4.2
154. Glassey, R.T., and Schaeffer, J., "The Relativistic Vlasov-Maxwell System in Two Space Dimensions: Part I", Arch. Ration. Mech. Anal., 141, 331-354, (1998). 4.2
155. Glassey, R.T., and Schaeffer, J., "The Relativistic Vlasov-Maxwell System in Two Space Dimensions: Part II", Arch. Ration. Mech. Anal., 141, 355-374, (1998). 4.2
156. Glassey, R.T., and Strauss, W., "Asymptotic stability of the relativistic Maxwellian", Publ. Res. Inst. Math. Sci., 29, 301-347, (1993). 4.2
157. Glimm, J., "Solutions in the large for nonlinear hyperbolic systems of equations", Commun. Pure Appl. Math., 18, 697-715, (1965). 4.1
158. Goliath, M., Nilsson, U.S., and Uggla, C., "Spatially self-similar spherically symmetric perfect-fluid models", Class. Quantum Grav., 15, 167-186, (1998). 3.3
159. Goliath, M., Nilsson, U.S., and Uggla, C., "Timelike self-similar spherically symmetric perfect-fluid models", Class. Quantum Grav., 15, 2841-2863, (1998). 3.3
160. Goode, S.W., and Wainwright, J., "Isotropic singularities in cosmological models", Class. Quantum Grav., 2, 99-115, (1985). 6.1
161. Grassin, M., "Global smooth solutions to Euler equations for a perfect gas", Indiana Univ. Math. J., 47, 1397-1432, (1998). 4.1
162. Gundlach, C., "Critical phenomena in gravitational collapse", Adv. Theor. Math. Phys., 2, 1-49, (1998). 3.3
163. Gundlach, C., "Critical Phenomena in Gravitational Collapse", Living Rev. Relativity, 2, lrr-1999-4, (1999). URL (cited on 22 December 1999): http://www. livingreviews.org/lrr-1999-4. 3.3
164. Guo, Y., "Smooth irrotational flows in the large to the Euler-Poisson system", Commun. Math. Phys., 195, 249-265, (1998). 4.1
165. Guo, Y., and Rein, G., "Isotropic steady states in stellar dynamics", Commun. Math. Phys., 219, 607-629, (2001). 4.2
166. Guo, Y., and Strauss, W., "Nonlinear instability of double-humped equilibria", Ann. Inst. Henri Poincare C, 12, 339-352, (1995). 7.2
167. Quo, Y., and Tahvildar-Zadeh, A.S., "Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics", in Chen, G.-Q., and DiBenedetto, E., eds., Nonlinear Partial Differential Equations, International Conference on Nonlinear Partial Differential Equations and Applications, March 21-24, 1998, Northwestern University, vol. 238 of Contemporary Mathematics, (American Mathematical Society, Providence, U.S.A., 1999). 4.1
168. Halliwell, J.J., "Scalar fields in cosmology with an exponential potential", Phys. Lett. B, 185, 341-344, (1987). 7.4
169. Hamilton, R., "Three manifolds of positive Ricci curvature", J. Differ. Geom., 17, 255-306, (1982). 7.2
170. Hartman, P., Ordinary Differential Equations, (Birkhäuser, Boston, U.S.A., 1982), 2nd edition. 1
171. Hauser, I., and Ernst, F.J., "Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation", Gen. Relativ. Gravit., 33, 195-293, (2001). 3.5
172. Heilig, U., "On the existence of rotating stars in general relativity", Commun. Math. Phys., 166, 457-493, (1995). 3.1
173. Heinzle, M., Rendall, A.D., and Uggla, C., "Theory of Newtonian self-gravitating stationary spherically symmetric systems", (August, 2004). URL (cited on 30 March 2005): http://arXiv.org/abs/math-ph/0408045. 3.1
174. Heinzle, M., Röhr, N., and Uggla, C., "Spherically symmetric relativistic stellar structures", Class. Quantum Grav., 20, 4567-4586, (2003). 3.1
175. Heinzle, M., Röhr, N., and Uggla, C., "Matter and dynamics in closed cosmologies", (June, 2004). URL (cited on 1 April 2005): http://arXiv.org/abs/math-ph/0406072. 7.3
176. Henkel, O., "Global prescribed mean curvature foliations in cosmological space-times. II", J. Math. Phys., 43, 2466-2485, (2001). Related online version (cited on 28 January 2002): http://arXiv.org/abs/gr-qc/ 0110082. 3.6
177. Henkel, O., "Global prescribed mean curvature foliations in cosmological space-times. I", J. Math. Phys., 43, 2439-2465, (2002). Related online version (cited on 28 January 2002): http://arXiv.org/abs/gr-qc/ 0110081. 3.6
178. Henkel, O., "Local prescribed mean curvature foliations in cosmological spacetimes", Math. Proc. Camb. Phil. Soc., 134, 551-571, (2003). Related online version (cited on 28 January 2002): http://arXiv.org/abs/ gr-qc/0108003. 3.6
179. Hertog, T., Horowitz, G.T., and Maeda, K., "Generic cosmic censorship violation in anti de Sitter space.", Phys. Rev. Lett., 92, 131101, (2004). 3.3
180. h", Class. Quantum Grav., 22, 607-634, (2005). 3.2
181. Heusler, M., Black Hole Uniqueness Theorems, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1996). 3.1
182. Heusler, M., "Stationary black holes: Uniqueness and beyond", Living Rev. Relativity, 1, lrr-1998-6, (1998). URL (cited on 12 December 1999): http://www.livingreviews.org/lrr-1998-6. 3.1
183. Hewitt, C., Horwood, J.T., and Wainwright, J., "Asymptotic dynamics of the exceptional Bianchi cosmologies", Class. Quantum Grau., 20, 1743-1756, (2003). 8.1
184. Hewitt, C., and Wainwright, J., "The asymptotic regimes of tilted Bianchi II cosmologies", Gen. Relativ. Gravit., 33, 65-94, (2001). 3.2
185. Hod, S., and Piran, T., "Mass inflation in dynamical collapse of a charged scalar field", Phys. Rev. Lett., 81, 1554-1557, (1998). 3.4
186. Hubbard, J.H., and West, B.H., Differential Equations: A Dynamical Systems Approach. Ordinary Differential Equations, vol. 5 of Texts in Applied Mathematics, (Springer, Berlin, 1991), 3rd edition. 1.
187. Isenberg, J.A., "Constant mean curvature solutions of the Einstein constraint equations on closed manifolds", Class. Quantum Grav., 12, 2249-2274, (1995). 2.1
188. 2-symmetric vacuum space-times", J. Math. Phys., 40, 340-352, (1999). 6.2
189. Isenberg, J.A., Mazzeo, R., and Pollack, D., "On the topology of vacuum spacetimes", Ann. Henri Poincare, 3, 369-383, (2003). 2.1
190. Isenberg, J.A., and Moncrief, V., "Asymptotic Behaviour of the
191. Isenberg, J.A., and Moncrief, V., "A set of nonconstant mean curvature solutions of the Einstein constraint equations on closed manifolds", Class. Quantum Grav., 13, 1819-1847, (1996). 2.1
192. Isenberg, J.A., and Moncrief, V., "Asymptotic behavior of polarized and half-polarized U(1) symmetric vacuum spacetimes", Class. Quantum Grav., 19, 5361-5386, (2002). 6.2
193. Isenberg, J.A., and Ó Murchadha, N., "Non CMC conformal data sets which do not produce solutions of the Einstein constraint equations", Class. Quantum Grav., 21, S233-S241, (2004). 2.1
194. Isenberg, J.A., and Rendall, A.D., "Cosmological spacetimes not covered by a constant mean curvature slicing", Class. Quantum Grav., 15, 3679-3688, (1998). 3.6
195. 2 symmetric spacetimes", Class. Quantum Grav., 20, 3783-3796, (2003). 3.6
196. Jensen, L.G., and Stein-Schabes, J.A., "Is inflation natural?", Phys. Rev. D, 35, 1146-1150, (1987). 7.6
197. John, F., Partial Differential Equations, vol. 1 of Applied Mathematical Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1982), 4th edition.
198. John, F., Nonlinear Wave Equations, Formation of Singularities, vol. 2 of University Lecture Series, (American Mathematical Society, Providence, U.S.A., 1990). 1
199. 3-models", Class. Quantum Grav., 20, 173-192, (2003). 3.6
200. Kichenassamy, S., "The blow-up problem for exponential nonlinearities", Commun. Part. Diff. Eq., 21, 125-162, (1996). 6.2
201. Kichenassamy, S., "Fuchsian equations in Sobolev spaces and blow-up", J. Differ. Equations, 125, 299-327, (1996). 6.2
202. Kichenassamy, S., Nonlinear Wave Equations, vol. 194 of Monographs and Textbooks in Pure and Applied Mathematics, (Marcel Dekker, New York, U.S.A., 1996). 1, 6.2
203. Kichenassamy, S., and Littman, W., "Blow-up surfaces for nonlinear wave equations, I", Commun. Part. Diff. Eq., 18, 431-452, (1993). 6.2
204. Kichenassamy, S., and Littman, W., "Blow-up surfaces for nonlinear wave equations, II", Commun. Part. Diff. Eq., 18, 1869-1899, (1993). 6.2
205. Kichenassamy, S., and Rendall, A.D., "Analytic description of singularities in Gowdy space-times", Class. Quantum Grav., 15, 1339-1355, (1998). 6.2
206. Kind, S., and Ehlers, J., "Initial boundary value problem for the spherically symmetric Einstein equations for a perfect fluid", Class. Quantum Grav., 18, 2123-2136, (1993). 2.6
207. Kitada, Y., and Maeda, K., "Cosmic no-hair theorem in power-law inflation", Phys. Rev. D, 45, 1416-1419, (1992). 7.4
208. Kitada, Y., and Maeda, K., "Cosmic no-hair theorem in homogeneous cosmological models. I. Bianchi models.", Class. Quantum Grav., 10, 703-734, (1993). 7.4
209. Klainerman, S., "A commuting vector fields approach to Strichartz-type inequalities and applications to quasi-linear wave equations", Int. Math. Res. Notices, 2001(5), 221-274, (2001). 2.4
210. 3+1", Ann. Math., 142, 39-119, (1995). 2.3, 3.3
211. Klainerman, S., and Nicolò, F., "On local and global aspects of the Cauchy problem in general relativity", Class. Quantum Grav., 16, R73-R157, (1999). 2.2, 5.2
212. Klainerman, S., and Nicolò, F., The evolution problem in general relativity, (Birkhäuser, Boston, U.S.A., 2003). 5.2
213. Klainerman, S., and Nicolò, F., "Peeling properties of asymptotically flat solutions to the Einstein vacuum equations", Class. Quantum Grav., 20, 3215-3257, (2003). 5.2
214. Klainerman, S., and Rodnianski, I., "Rough solution for the Einstein vacuum equations", (September, 2001). URL (cited on 1 March 2002): http://arXiv.org/abs/math.AP/0109173. 2.4
215. Klainerman, S., and Rodnianski, I., "Causal geometry of Einstein-vacuum spacetimes with finite curvature flux", (September, 2003). URL (cited on 30 March 2005): http://arXiv.org/abs/math.AP/0309459. 2.4
216. Klainerman, S., and Rodnianski, I., "A geometric approach to the Littlewood-Paley theory", (September, 2003). URL (cited on 30 March 2005): http://arXiv.org/abs/math.AP/0309463. 2.4
217. Kleihaus, B., and Kunz, J., "Static axially symmetric Einstein-Yang-Mills-dilaton solutions: I. Regular solutions", Phys. Rev. D, 57, 834-856, (1998). 3.1
218. Krieger, J., "Stability of spherically symmetric wave maps", (March, 2005). URL (cited on 30 April 2005): http://arXiv.org/abs/math.AP/ 0503048. 3.5
219. Kunze, M., and Rendall, A.D., "Simplified models of electromagnetic and gravitational radiation damping.", Class. Quantum Grav., 18, 3573-3587, (2001). 9.2
220. Kunze, M., and Rendall, A.D., "The Vlasov-Poisson system with radiation damping.", Ann. Henri Poincare, 2, 857-886, (2001). 9.2
221. LeBlanc, V.G., "Asymptotic states of magnetic Bianchi I cosmologies", Class. Quantum Grav., 14, 2281-2301, (1997). 7.1, 8.1
222. LeBlanc, V.G., "Bianchi II magnetic cosmologies", Class. Quantum Grav., 15, 1607-1626, (1998). 7.1
223. 0 cosmologies", Class. Quantum Grav., 12, 513-541, (1995). 7.1
224. Lee, H., "Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant", Math. Proc. Camb. Phil. Soc., 137, 495-509, (2004). 7.3
225. Lee, H., "The Einstein-Vlasov system with a scalar field", (April, 2004). URL (cited on 30 March 2005): http://arXiv.org/abs/gr-qc/0404007. 7.4
226. Lifshitz, E.M., and Khalatnikov, I.M., "Investigations in relativistic cosmology", Adv. Phys., 12, 185-249, (1963). 3.2
227. Lim, W.C., van Elst, H., Uggla, C., and Wainwright, J., "Asymptotic isotropization in inhomogeneous cosmology", Phys. Rev. D, 69, 103507, (2004). 7.6, 8.2
228. Lin, S.S., "Stability of gaseous stars in spherically symmetric motions", SIAM J. Math. Anal., 28, 539-569, (1997). 4.1
229. Lin, X.F., and Wald, R.M., "Proof of the closed universe recollapse conjecture for general Bianchi type IX cosmologies", Phys. Rev. D, 41, 2444-2448, (1990). 7.3
230. Lindblad, H., "Well-posedness for the linearized motion of a compressible fluid with free surface boundary", Commun. Math. Phys., 236, 281-310, (2003). 2.0
231. Lindblad, H., "Well-posedness for the motion of an incompressible liquid with free surface boundary", (February, 2004). URL (cited on 29 March 2005): http://arXiv.org/abs/math.AP/0402327. 2.6
232. Lindblad, H., and Rodnianski, I., "The weak null condition for Einstein's equations.", C. R. Acad. Sci., 336, 901-906, (2003). 5.2
233. Lindblad, H., and Rodnianski, I., "The global stability of the Minkowski space-time in harmonic gauge", (November, 2004). URL (cited on 29 March 2005): http://arXiv.org/abs/math.AP/0411109. 5.2
234. Lindblom, L., and Masood-ul Alam, A.K.M., "On the spherical symmetry of static stellar models", Commun. Math. Phys., 162, 123-145, (1994). 3.1
235. Lions, P.-L., "Compactness in Boltzmann's equation via Fourier integral operators and applications", J. Math. Kyoto Univ., 34, 391-427, (1994). 4.2
236. Lions, P.-L., and Perthame, B., "Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system", Invent. Math., 105, 415-430, (1991). 4.2
237. Longair, M.S., Galaxy Formation, Astronomy and Astrophysics Library, (Springer, Berlin, Germany; New York, U.S.A., 1998). 7.2
238. Maartens, R., "Brane-World Gravity", Living Rev. Relativity, 7, lrr-2004-7, (2004). URL (cited on 22 April 2005): http://www.livingreviews.org/ lrr-2004-7. 7.5
239. Majda, A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, vol. 53 of Applied Mathematical Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1984). 1
240. Makino, T., "On spherically symmetric stellar models in general relativity", J. Math. Kyoto Univ., 38, 55-69, (1998). 3.1, 4.1
241. Makino, T., "On the spiral structure of the (R,M) diagram for a stellar model of the Tolman-Oppenheimer-Volkoff equation", Funkcialaj Ekvacioj, 43, 471-489, (2000). 3.1
242. Martín-García, J.M., and Gundlach, C., "Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system", Phys. Rev. D, 65, 084026-1-18, (2002). Related online version (cited on 17 January 2002): http://arXiv.org/abs/gr-qc/0112009. 3.3
243. Maxwell, D., "Rough solution of the Einstein constraint equations", (May, 2004). URL (cited on 15 February 2005): http://arXiv.org/abs/gr-qc/0405088. 2.1, 2.4
244. Maxwell, D., "Solutions of the Einstein constraint equations with apparent horizon boundaries", Commun. Math. Phys., 253, 561-583, (2004). 2.1
245. Misner, C.W., "Mixmaster Universe", Phys. Rev. Lett., 22, 1071-1074, (1967). 8.1
246. 3 × R Topology", Ann. Phys. (N.Y.), 132, 87-107, (1981). 3.6
247. Moncrief, V., "Neighbourhoods of Cauchy horizons in cosmological spacetimes with one Killing field", Ann. Phys. (N.Y.), 141, 83-103, (1982). 6.2
248. Moncrief, V., and Eardley, D.M., "The global existence problem and cosmic censorship in general relativity", Gen. Relativ. Gravit., 13, 887-892, (1981). l
249. Moss, I., and Sahni, V., "Anisotropy in the chaotic inflationary universe", Phys. Lett. B, 178, 159-162, (1986). 7.4
250. Mucha, P.B., "Global existence for the Einstein-Boltzmann equation in flat Robertson-Walker spacetime", Commun. Math. Phys., 203, 107-118, (1999). 4.2
251. Müller, V., Schmidt, H.-.J., and Starobinsky, A.A., "Power-law inflation as an attractor solution for inhomogeneous cosmological models.", Class. Quantum Grav., 7, 1163-1168, (1990). 7.6
252. 3-Gowdy spacetimes with stringy matter", Class. Quantum Grav., 19, 6279-6288, (2002). 3.6
253. 3-Gowdy symmetric IIB superstring cosmology", Class. Quantum Grav., 20, 4983-4994, (2003). 3.6
254. Narita, M., "Global properties of higher-dimensional cosmological spacetimes", Class. Quantum Grav., 21, 2071-2088, (2004). 3.6, 6.2
255. Narita, M., "On initial conditions and global existence for accelerating cosmologies from string theory", (February, 2005). URL (cited on 18 March 2005): http://arXiv.org/abs/gr-qc/0502116. 3.6, 6.2
256. Narita, M., Torii, T., and Maeda, K., "Asymptotic singular behavior of Gowdy spacetimes in string theory", Class. Quantum Grav., 17, 4597-4613, (2000). 6.2
257. Newman, R.P.A.C., "On the structure of conformal singularities in classical general relativity", Proc. R. Soc. London, Ser. A, 443, 473-492, (1993). 6.1
258. Newman, R.P.A.C., "On the structure of conformal singularities in classical general relativity. II Evolution equations and a conjecture of K. P. Tod", Proc. R. Soc. London, Ser. A, 443, 493-515, (1993). 6.1
259. 0 models - the radiation fluid.", Class. Quantum Grav., 17, 3119-3134, (2000). 3.2
260. Noundjeu, P., and Noutchegueme, N., "Local existence and continuation criterion for solutions of the spherically symmetric Einstein-Vlasov-Maxwell system", Gen. Relativ. Gravit., 36, 1373-1398, (2004). 3.3
261. Noundjeu, P., Noutchegueme, N., and Rendall, A.D., "Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system", J. Math. Phys., 45, 668-676, (2004). 3.3
262. Noutchegueme, N., Dongo, D., and Takou, E., "Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi type I space-time", (March, 2005). URL (cited on 13 April 2005): http://arXiv.org/abs/gr-qc/0503048. 4.2
263. Noutchegueme, N., and Tetsadjio, M.E., "Global solutions for the relativistic Boltzmann equation in the homogeneous case on the Minkowski space-time", (July, 2003). URL (cited on 13 April 2005): http://arXiv.org/abs/gr-qc/0307065. 4.2
264. Olabarrieta, I., and Choptuik, M.W., "Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry", Phys. Rev. D, 65, 024007-1-10, (2002). 3.3
265. Park, J., "Static solutions of the Einstein equations for spherically symmetric elastic bodies", Gen. Relativ. Gravit., 32, 235-252, (2000). 3.1
266. Pfaffelmoser, K., "Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data", J. Differ. Equations, 95, 281-303, (1992). 4.2
267. Poisson, E., and Israel, W., "Internal structure of black holes", Phys. Rev. D, 41, 1796-1809, (1990). 3.4
268. Price, R., "Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations.", Phys. Rev. D, 5, 2419-2438, (1972). 3.4
269. Racke, R., Lectures on Nonlinear Evolution Equations: Initial Value Problems, vol. 19 of Aspects of Mathematics, (Vieweg, Wiesbaden, Germany, 1992). 1
270. Rein, G., "Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics", Commun. Math. Phys., 135, 41-78, (1990). 4.2
271. Rein, G., "Static solutions of the spherically symmetric Vlasov-Einstein system", Math. Proc. Camb. Phil. Soc., 115, 559-570, (1994). 3.1
272. Rein, G., "Cosmological solutions of the Vlasov-Einstein system with spherical, plane and hyperbolic symmetry", Math. Proc. Camb. Phil. Soc., 119, 739-762, (1996). 3.6, 8.2
273. Rein, G., "Nonlinear Stability of Homogeneous Models in Newtonian Cosmology", Arch. Ration. Mech. Anal., 140, 335-351, (1997). 9.3
274. Rein, G., "Static shells for the Vlasov-Poisson and Vlasov-Einstein systems", Indiana Univ. Math. J., 48, 335-346, (1999). 3.1, 3.3
275. Rein, G., "Stationary and static stellar dynamical models with axial symmetry", Nonlinear Anal., 41, 313-344, (2000). 3.1
276. Rein, G., "Non-linear stability of gaseous stars,", Arch. Ration. Mech. Anal., 168, 115-130, (2003). 4.1
277. Rein, G., "On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry", Math. Proc. Camb. Phil. Soc., 137, 237-244, (2004). 7.2
278. Rein, G., and Rendall, A.D., "Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data", Commun. Math. Phys., 150, 561-583, (1992). 3.3
279. Rein, G., and Rendall, A.D., "Smooth static solutions of the spherically symmetric Vlasov-Einstein system", Ann. Inst. Henri Poincare A, 59, 383-397, (1993). 3.1.
280. Rein, G., and Rendall, A.D., "Global Existence of Classical Solutions to the Vlasov-Poisson System in a Three Dimensional, Cosmological Setting", Arch. Ration. Mech. Anal., 126, 183-201, (1994). 4.2, 9.3
281. Rein, G., and Rendall, A.D., "Compact support of spherically symmetric equilibria in relativistic and non-relativistic galactic dynamics", Math. Proc. Camb. Phil. Soc., 128, 363-380, (2000). 3.1
282. Rein, G., Rendall, A.D., and Schaeffer, J., "A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system", Commun. Math. Phys., 168, 467-478, (1995). 3.3
283. Rein, G., Rendall, A.D., and Schaeffer, J., "Critical collapse of collisionless matter: A numerical investigation", Phys. Rev. D, 58, 044007-1-8, (1998). 3.3
284. Rendall, A.D., "Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations", Proc. R. Soc. London, Ser. A, 427, 221-239, (1990). 9.4
285. Rendall, A.D., "The initial value problem for a class of general relativistic fluid bodies", J. Math. Phys., 33, 1047-1053, (1992). 2.6
286. Rendall, A.D., "On the definition of post-Newtonian approximations", Proc. R. Soc. London, Ser. A, 438, 341-360, (1992). 9.2
287. Rendall, A.D., "Cosmic censorship for some spatially homogeneous cosmological models", Ann. Phys. (N.Y.), 233, 82-96, (1994). 7.8
288. Rendall, A.D., "The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system", Commun. Math. Phys., 163, 89-112, (1994). 9.2
289. Rendall, A.D., "Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry", Class. Quantum Grav., 12, 1517-1533, (1995). 3.6
290. Rendall, A.D., "Global properties of locally homogeneous cosmological models with matter.", Math. Proc. Camb. Phil. Soc., 118, 511-526, (1995). 7.1, 7.3
291. Rendall, A.D., "On the nature of singularities in plane symmetric scalar field cosmologies.", Gen. Relativ. Gravit., 27, 213-221, (1995). 8.2
292. Rendall, A.D., "Constant mean curvature foliations in cosmological spacetimes", Helv. Phys. Acta, 69, 490-500, (1996). 2.1, 3.6
293. Rendall, A.D., "The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I", J. Math. Phys., 37, 438-451, (1996). 7.1
294. Rendall, A.D., "Existence and non-existence results for global constant mean curvature foliations", Nonlinear Anal., 30, 3589-3598, (1997). 3.6
295. Rendall, A.D., "Existence of Constant Mean Curvature Foliations in Spacetimes with Two-Dimensional Local Symmetry", Commun. Math. Phys., 189, 145-164, (1997). 3.6
296. Rendall, A.D., "Global dynamics of the mixmaster model", Class. Quantum Grav., 14, 2341-2356, (1997). 3.2
297. Rendall, A.D., "An introduction to the Einstein-Vlasov system", in Chruściel, P.T., ed., Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations, Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, February 29 - March 30, 1996, vol. 41 of Banach Center Publications, 35-68, (Polish Academy of Sciences, Institute of Mathematics, Warsaw, Poland, 1997). 3.3
298. Rendall, A.D., "Solutions of the Einstein equations with matter", in Francaviglia, M., Longhi, G., Lusanna, L., and Sorace, E., eds., General Relativity and Gravitation, Proceedings of the 14th International Conference on General Relativity and Gravitation, Florence, Italy, 6-12 August 1995, 313-335, (World Scientific, Singapore; River Edge, U.S.A., 1997). 3.1
299. Rendall, A.D., "Blow-up for solutions of hyperbolic PDE and spacetime singularities", in Depauw, N., Robert, D., and Saint-Raymond, X., eds., Proceedings of Journées Equations aux Dérivées Partielles, La Chapelle sur Erdre, Nantes, France, 5-9 June 2000, XIV-1-12, (University of Nantes, Nantes, France, 2000). Related online version (cited on 1 March 2002): http://www.numdam.org/item?id=JEDP_2000_A14_0. 6.2
300. Rendall, A.D., "Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity", Class. Quantum Grav., 17, 3305-3316, (2000). 6.2
301. Rendall, A.D., "Collection of equations", personal homepage, Max Planck Institute for Gravitational Physics, (2002). URL (cited on 30 March 2005): http://www.aei.mpg.de/~rendall/3+1.ps. 1
302. Rendall, A.D., "Cosmological Models and Centre Manifold Theory", Gen. Relativ. Gravit., 34, 1277-1294, (2002). Related online version (cited on 21 January 2002): http://arXiv.org/abs/gr-qc/0112040. 3.2, 7.4
303. Rendall, A.D., "Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound", Class. Quantum Grow., 21, 2445-2454, (2004). 7.3, 7.4, 7.4
304. Rendall, A.D., "Asymptotics of solutions of the Einstein equations with positive cosmological constant.", Ann. Henri Poincare, 5, 1041-1064, (2004). 5.1, 6.3, 7.6
305. Rendall, A.D., "Mathematical properties of cosmological models with accelerated expansion", (August, 2004). URL (cited on 30 March 2005): http://arXiv.org/abs/gr-qc/0408053. 7, 7.5
306. Rendall, A.D., "Intermediate inflation and the slow-roll approximation", Class. Quantum Grav., 22, 1655-1666, (2005). 7.4
307. Rendall, A.D., and Schmidt, B.G., "Existence and properties of spherically symmetric static fluid bodies with given equation of state", Class. Quantum Grav., 8, 985-1000, (1991). 3.1
308. Rendall, A.D., and Tod, K.P., "Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric", Class. Quantum Grav., 16, 1705-1726, (1999). 3.2
309. Rendall, A.D., and Uggla, C., "Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations", Class. Quantum Grav., 17, 4697-4713, (2000). 3.2
310. Rendall, A.D., and Weaver, M., "Manufacture of Gowdy spacetimes with spikes", Class. Quantum Grav., 18, 2959-2975, (2001). 8.3, 8.4
311. Ringström, H., "The Bianchi IX attractor", Ann. Henri Poincare, 2, 405-500, (2000). 3.2, 8.1
312. Ringström, H., "Curvature blow up in Bianchi VIII and IX vacuum spacetimes", Class. Quantum Grav., 17, 713-731, (2000). 3.2, 8.1
313. Ringström, H., "The future asymptotics of Bianchi VIII vacuum solutions", Class. Quantum Grav., 18, 3791-3824, (2001). 7.1
314. Ringström, H., "Future asymptotic expansions of Bianchi VIII vacuum metrics", Class. Quantum Grav., 20, 1943-1990, (2003). 7.1
315. Ringström, H., "Asymptotic expansions close to the singularity in Gowdy spacetimes", Class. Quantum Grav., 21, S305-S322, (2004). 8.2
316. Ringström, H., "On a wave map equation arising in general relativity", Commun. Pure Appl. Math., 57, 657-703, (2004). 3.6, 7.2, 8.4
317. Ringström, H., "On Gowdy vacuum spacetimes", Math. Proc. Camb. Phil. Soc., 136, 485-512, (2004). 8.2
318. Schaeffer, J., "A class of counterexamples to Jeans' theorem for the Vlasov-Einstein system", Commun. Math. Phys., 204, 313-327, (1999). 3.1
319. Secchi, P., "On the equations of viscous gaseous stars", Ann. Scuola Norm. Sup. Pisa, 18, 295-318, (1991). 2.6
320. Shapiro, S.L., and Teukolsky, S.A., "Relativistic stellar dynamics on the computer. II. Physical applications", Astrophys. J., 298, 58-79, (1985). 3.1
321. Shapiro, S.L., and Teukolsky, S.A., "Scalar gravitation - a laboratory for numerical relativity", Phys. Rev. D, 47, 1529-1540, (1993). 4.2
322. Sideris, T., "Formation of singularities in three-dimensional compressible fluids", Commun. Math. Phys., 101, 475-485, (1979). 4.1
323. Smoller, J.A., and Temple, B., "Global solutions of the relativistic Euler equations", Commun. Math. Phys., 156, 65-100, (1993). 4.1
324. Smoller, J.A., Wasserman, A.G., Yau, S.-T., and McLeod, J.B., "Smooth static solutions of the Einstein-Yang-Mills equations", Commun. Math. Phys., 143, 115-147, (1991). 3.1
325. 3 Gowdy models", Class. Quantum Grav., 19, 4483-4504, (2002). Related online version (cited on 31 January 2002): http://arXiv.org/abs/gr-qc/0109011. 6.2
326. Starobinsky, A.A., "Isotropization of arbitrary cosmological expansion given an effective cosmological constant", J. Exp. Theor. Phys. Lett., 37, 66-69, (1983). 6.3, 7.6
327. Strauss, W., Nonlinear Wave Equations, vol. 73 of Regional Conference Series in Mathematics, (American Mathematical Society, Providence, U.S.A., 1989). 1
328. Struwe, M., "Equivariant wave maps in two space dimensions.", Commun. Pure Appl. Math., 56, 815-823, (2003). 3.3
329. Stuart, D.M.A., "Geodesics and the Einstein nonlinear wave system", J. Math. Pures Appl., 83, 541-587, (2004). 9.6
330. Tanimoto, M., "Linear perturbations of spatially locally homogeneous spacetimes", in Duggal, K.L., and Sharma, R., eds., Recent Advances in Riemannian and Lorentzian Geometries, vol. 337 of Contemporary Mathematics, 171-185, (American Mathematical Society, Providence, U.S.A., 2003). 7.2
331. Tanimoto, M., "Harmonic analysis of linear fields on the nilgeometric cosmological model", J. Math. Phys., 45, 4896-4919, (2004). 7.2
332. 2 × R geometric spacetimes and linear perturbations", Class. Quantum Grav., 21, 5355-5374, (2004). 7.2
333. Tao, T., "Geometric renormalization of large energy wave maps", (November, 2004). URL (cited on 30 March 2005): http://arXiv.org/abs/math.AP/ 0411354. 2.4
334. Taylor, M.E., Pseudodifferential Operators and Nonlinear PDE, vol. 100 of Progress in Mathematics, (Birkhäuser, Boston, U.S.A., 1991). 2.3
335. Taylor, M.E., Partial Differential Equations, 3 vols., Applied Mathematical Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1996). 1
336. Tchapnda, S.B., "Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system", Class. Quantum Grav., 21, 5333-5346, (2004). 3.6, 8.2
337. Tchapnda, S.B., and Noutchegueme, N., "The surface-symmetric Einstein-Vlasov system with cosmological constant.", (April, 2003). URL (cited on 17 April 2005): http://arXiv.org/abs/gr-qc/0304098. 3.6, 7.6
338. Tchapnda, S.B., and Rendall, A.D., "Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant", Class. Quantum Grav., 20, 3037-3049, (2003). 3.6, 7.6
339. Tegankong, D., "Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry", (January, 2005). URL (cited on 17 March 2005): http://arXiv.org/abs/gr-qc/0501062. 7.2
340. Tegankong, D., Noutchegueme, N., and Rendall, A.D., "Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry", J. Hyperbol. Differ. Equations, 1, 691-724, (2004). 7.6
341. Thurston, W., Three-dimensional geometry and topology, Vol. 1, vol. 35 of Princeton Mathematical Series, (Princeton University Press, Princeton, U.S.A., 1997). 7.2
342. Tod, K.P., "Isotropic cosmological singularities: other matter models", Class. Quantum Grav., 20, 521-534, (2003). 6.1
343. van der Bij, J.J., and Radu, E., "On rotating regular nonabelian solitons", Int. J. Mod. Phys. A, 17, 1477-1490, (2002). 3.1
344. Wainwright, J., and Ellis, G.F.R., Dynamical Systems in Cosmology, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1997). 3.2, 7.1
345. Wainwright, J., Hancock, M.J., and Uggla, C., "Asymptotic self-similarity breaking at late times in cosmology", Class. Quantum Grav., 16, 2577-2598, (1999). 3.2
346. Wald, R.M., "Asymptotic behaviour of homogeneous cosmological models with cosmological constant", Phys. Rev. D, 28, 2118-2120, (1983). 7.3
347. 0 cosmologies.", Class. Quantum Grav., 17, 421-434, (2000). 3.2
348. 2 symmetric spacetimes with Vlasov matter", Class. Quantum Grav., 21, 1079-1098, (2004). 3.6
349. Witt, D., "Vacuum spacetimes that admit no maximal slice", Phys. Rev. Lett., 57, 1386-1389, (1986). 2.1
350. Wolansky, G., "Static Solutions of the Vlasov-Einstein System", Arch. Ration. Mech. Anal., 156, 205-230, (2001). 4.2
351. Woodhouse, N.M.J., "Integrability and Einstein's equations", in Chruściel, P.T., ed., Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations, Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, Poland, February 29 - March 30, 1996, vol. 41 of Banach Center Publications, 221-232, (Polish Academy of Sciences, Institute of Mathematics, Warsaw, Poland, 1997). 3.5
352. Wu, S., "Well-posedness in Sobolev spaces of the full water wave problem in 3-D", J. Amer. Math. Soc., 12, 445-495, (1999). 2.6
353. York Jr, J.W., "Conformal "Thin-Sandwich" Data for the Initial-Value Problem of General Relativity", Phys. Rev. Lett., 82, 1350-1353, (1999). 2.1
354. Zipser, N., The global nonlinear stability of the trivial solution of the Einstein-Maxwell equations, Ph.D. Thesis, (Harvard University, Cambrige, U.S.A., 2000). 5.2