Is general relativity 'essentially understood' ?

Annalen der Physik (Leipzig)

Volumn 15, Issue 1-2, 2006, Pages 84-108

  Friedrich, Helmut ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Asymptotic structure; Classical black holes; Classical general relativity; Initial value problem for Einstein's field equations; Numerical relativity; Singularities and cosmic censorship

Indexed keywords

ASTROPHYSICS; GRAVITATION; INFORMATION ANALYSIS; NUMERICAL ANALYSIS;

EINSTEIN'S THEORY OF GRAVITATION; FIELD EQUATIONS; GRAVITATIONAL WAVE;

RELATIVITY;

EID: 31144475275     PISSN: 00033804     EISSN: 15213889     Source Type: Journal    
DOI: 10.1002/andp.200510173     Document Type: Conference Paper

References (146)

1. M. Alcubierre, B. Brügmann, M. Miller, and W.-M. Suen, Phys. Rev. D 60, 064017 (1999).
2. E.W. Allen, E. Buckmiller, L.M. Burko, and R.H. Price, Phys. Rev. D 70, 044038 (2004).
3. M. T. Anderson, Existence and stability of even dimensional asymptotically de Sitter spaces. http://xxx.lanl.gov/abs/gr-qc/0408072.
4. M.T. Anderson and P.T. Chruściel, Asymptotically simple solutions of the vacuum Einstein equations in even dimensions, http://xxx.lanl.gov/abs/gr-qc/0412020.
5. L. Andersson, The global existence problem in general relativity, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
6. L. Andersson and P.T. Chruściel, Commun. Math. Phys. 161, 533-568 (1994).
7. L. Andersson, P. T. Chruściel, Solutions of the constraint equations in general relativity satisfying hyperboloidal boundary conditions. Dissertationes Mathematicae Polska Akademia Nauk, Inst. Matern., Warszawa, 1996.
8. L. Andersson, P.T. Chruściel, and H. Friedrich, Commun. Math. Phys. 149, 587-612 (1992).
9. L. Andersson, H. van Elst, and C. Uggla, Class. Quantum. Gravity 21, S29-S57 (2004).
10. L. Andersson, H. van Elst, W. Lim, and C. Uggla, Phys. Rev. Lett. 94, 051101 (2005).
11. L. Andersson and V. Moncrief, Ann. Henri Poincaré 4, 1-34 (2003).
12. L. Andersson, V. Moncrief, Future complete vacuum space-times, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
13. R. Bartnik, Commun. Pure Appl. Math. 39, 661-693 (1986).
14. R. Bartnik and J. McKinnon, Phys. Rev. Lett. 61, 141-144 (1988).
15. R. Bartnik and J. Isenberg, The constraint equations, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
16. T. Baumgarte and S. Shapiro, Phys. Rev. D 59, 024007 (1999).
17. R. Beig and N. O'Murchadha, Phys. Rev. Lett. 66, 2421-2424 (1991).
18. R. Beig and N. O'Murchadha, Class. Quantum Gravity 11, 419-430 (1994).
19. V. Belinskii, I. Khalatnikov, and E. Lifshitz, Adv. in Phys. 19, 525-573 (1970).
20. V. Belinskii, I. Khalatnikov, and E. Lifshitz, Adv. in Phys. 31, 639-667 (1982).
21. B. Berger, Numerical Approaches to Space-Time Singularities. Living Reviews in Relativity 2002.
22. B. Berger, D. Garfinkle, and E. Strasser, Class. Quantum Gravity 14 L29-L36 (1997).
23. B. Berger and V. Moncrief, Phys. Rev. D 48, 4676-4687 (1993).
24. P. Bizoń Acta Phys. Polonica B 33, 1893-1922 (2002).
25. P. Bizoń and Z. Tabor, Phys. Rev. D 64, 121701-1-121701-4 (2001).
26. H. Bondi, M. G. J. van der Burg, and A.W. K. Metzner, Proc. Roy. Soc. A 269, 21-52 (1962).
27. T. Brainerd and C. Kochanek (eds.), Gravitational Lensing: Recent Progress and Future Go. ASP Conference Series, Vol. CS-237, 2001.
28. H. L. Bray, J. Diff. Geom. 59, 177-267 (2001).
29. H. Bray and P. Chruściel, The Penrose inequality, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
30. O. Brodbeck, S. Fritelli, P. Hübner, and O. Reula, J. Math. Phys. 40, 909-923 (1999).
31. B. Carter, Has the black hole equilibrium problem been solved?, in: The Eighth Marcel Grossmann Meeting, edited by T. Piran and R. Ruffini (World Scientific, Singapore, 1999).
32. M. Chae and P. Chruściel, Commun. Pure Appl. Math. 57, 1015-1074 (2004).
33. Y. Choquet-Bruhat, Future complete U(1) symmetric Einsteinian space-times, the unpolarized case, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P. T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
34. Y. Choquet-Bruhat and R. Geroch, Commun. Math. Phys. 14, 329-335 (1969).
35. Y. Choquet-Bruhat and J.W. York, The Cauchy problem, in: General Relativity and Gravitation, edited by A. Held, Vol. 1 (New York, Plenum, 1980).
36. M.W. Choptuik, Phys. Rev. Lett. 70, 9 (1993).
37. D. Christodoulou, Ann. Math. 149, 183-217 (1999).
38. D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space (Princeton University Press, Princeton, 1993).
39. P. T. Chruściel, Black holes, in: The Conformal Structure of Space-Time, edited by J. Frauendiener and H. Friedrich (Springer, Berlin, 2002).
40. P. T. Chruściel and E. Delay, Class. Quantum Gravity 19, L71-L79 (2002); Erratum, Class. Quantum Gravity 19, 3389 (2002).
41. P.T. Chruściel and E. Delay, On mapping properties of the general relativistic constraints operator in weighted function spaces, with application. Mém. Soc. Math. France, submitted, http://xxx.lanl.gov/abs/gr-qc/0301073.
42. P.T. Chruściel and J. Isenberg, Phys. Rev. D 48, 1616-1628 (1993).
43. P.T. Chruściel, J. Isenberg, and D. Pollack, Phys. Rev. Lett. 93, 081101 (2004).
44. P.T. Chruściel and K. Lake, Class. Quantum Gravity 21, S153-S170 (2004).
45. P.T. Chruściel and A. Rendall, Ann. Phys. 242, 349-385 (1995).
46. C. Clarke, G. Ellis, and F. Tipler, Singularities and Horizons - A Review Article, in: General Relativity and Gravitation, Vol. 2, edited by A. Held (Plenum, New York, 1980).
47. J. Corvino, Commun. Math. Phys. 214, 137-189 (2000).
48. J. Corvino and R. Schoen, On the Asymptotics for the Vacuum Einstein Constraint Equations. http://xxx.lanl.gov/abs/gr-qc/0301071.
49. C. Cutler and R.M. Wald, Class. Quantum Gravity 6, 453-466 (1989).
50. M. Dafermos, Black hole formation from a complete past. arXiv:gr-qc/0310040.
51. M. Dafermos and I. Rodnianski, A Proof of Price's law for the collapse of a self-gravitating scalar field. arXiv:gr-qc/0309115.
52. M. Dafermos and I. Rodnianski, A note on boundary value problems for black hole evolutions. http://xxx.lanl.gov/abs/gr-qc/0403034.
53. S. Dain, Class. Quantum Gravity 21, 555-573 (2004).
54. S. Dain, Phys. Rev. Lett. 93, 231101 (2004).
55. S. Dain and H. Friedrich, Commun. Math. Phys. 222, 569-609 (2001).
56. S. Dain, J. Jaramillo, and B. Krishnan, On the existence of initial data containing isolated black holes, gr-qc/0412061 (2004).
57. S. Dain and G. Nagy, Phys. Rev. D 65, 084020-1 (2002).
58. A. Einstein Ann. Phys. 49, 769-822 (1916).
59. A. Einstein, Näherungsweise Integration der Feldgleichungen der Gravitation. Sitzungsberichte Königl. Preuss. Akademie der Wiss. (1916), pp. 688-696.
60. A. Einstein, Über Gravitationswellen. Sitzungsberichte Königl. Preuss. Akademie der Wiss. (1918), pp. 154-167.
61. A. Fischer and J. Marsden, The initial value problem and the dynamical formulation of general relativity, in: General relativity. An Einstein centenary survey, edited by S. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979).
62. Y. Fourès-Bruhat, Acta Mathematica 88, 141-225 (1952).
63. J. Frauendiener, Conformal infinity. Living reviews, 2002. http://www.livingreviews.org/lrr-2004-1.
64. J. Frauendiener and T. Vogel, Class. Quantum Gravity 22, 1769-1793 (2005).
65. H. Friedrich, Commun. Math. Phys. 100, 525-543 (1985).
66. H. Friedrich, Commun. Math. Phys. 103, 35-65 (1986).
67. H. Friedrich, Commun. Math. Phys. 107, 587-609 (1986).
68. H. Friedrich, J. Differ. Geom. 34, 275-345 (1991).
69. H. Friedrich, J. Geom. Phys. 17, 125-184 (1995).
70. H. Friedrich, J. Geom. Phys. 24, 83-163 (1998).
71. H. Friedrich, Conformal Einstein evolution, in: The Conformal Structure of Spacetime: Geometry, Analysis, Numerics, edited by J. Frauendiener and H. Friedrich (Springer, Berlin, 2002).
72. H. Friedrich, Class. Quantum. Gravity 20, 101-117 (2003).
73. H. Friedrich, Commun. Math. Phys. 235, 513-543 (2003).
74. H. Friedrich, Smoothness at null infinity and the structure of initial data, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
75. H. Friedrich, Class. Quantum Gravity 22, L77-L82 (2005).
76. H. Friedrich and G. Nagy, Commun. Math. Phys. 201, 619-655 (1999).
77. H. Friedrich and A. Rendall, The Cauchy Problem for the Einstein Equations, in: Einstein's Field Equations and Their Physical Implications, edited by B. Schmidt (Lecture Notes in Physics, vol. 540, Springer, Berlin 2000).
78. S. Frittelli and O. Reula, J. Math. Phys. 40, 5143-5156 (1999).
79. V. Frolov and I. Novikov, Black Hole Physics (Kluwer, Dordrecht, 1998).
80. D. Garfinkle, Numerical simulations of generic singularities. arXiv:gr-qc/0312117 v2.
81. C. Gundlach, Phys. Rep. 367, 339-405 (2003).
82. C. Gundlach, G. Calabrese, and I. Hinder, Constraint damping in the Z4 formulation and harmonic gauge. http://xxx.lanl.gov/abs/gr-qc/0504114.
83. C. Gundlach, R. Price, and J. Pullin, Phys. Rev. D 49, 883 (1994);
84. Phys. Rev. D 49, 890 (1994).
85. S. Hawking and G. Ellis, The large scale structure of space-time (Cambridge University Press, Cambridge, 1973).
86. S. Hawking and R. Penrose, Proc. Roy. Soc. A 314, 529-548 (1970).
87. S. Hollands and R. Wald, Conformal infinity does not exist for radiating solutions in odd space-time dimensions. gr-qc/0407014.
88. P. Hübner, Class. Quantum Gravity 18, 1871-1884 (2001).
89. T. Hughes, T. Kato, and J. Marsden, Arch. Ration. Mech. Anal. 63, 273-294 (1977).
90. G. Huisken and T. Ilmanen, J. Diff. Geom. 59, 353-437 (2001).
91. S. Husa, Problems and successes in the numerical approach to the conformal field equations, in: The Conformal Structure of Spacetime: Geometry, Analysis, Numerics, edited by J. Frauendiener and H. Friedrich (Springer, Berlin, 2002).
92. J. Isenberg, R. Mazzeo, and D. Pollack, Ann. Henri Pioncaré 4, 369-383 (2003).
93. W. Israel, Dark stars: the evolution of an idea, in: Three hundred years of gravitation, edited by S. Hawking and W. Israel (Cambridge University Press, Cambridge, 1989).
94. W. Israel, The internal structure of black holes, in: Black Holes and Relativistic Stars, edited by R. M. Wald (University of Chicago Press, Chicago, 1998).
95. S. Klainerman and F. Nicolò, The Evolution Problem in General Relativity. (Birkhäuser, Basel, 2003).
96. S. Klainerman and F. Nicolò, Class. Quantum Gravity 20, 3215-3257 (2003).
97. S. Klainerman and I. Rodnianski Causal geometry of Einstein vacuum space-times with finite curvature flux. math.ap/0308123 (2003).
98. M. Kramer et al., The double pulsar - A new testbed for relativistic gravity. Binary Radio Pulsars, ASP Conference Series, Vol. TBD, 2004, edited by F.A. Rasio and I.H. Stairs, arXiv: astro-ph/0405179.
99. J. Lee and T. Parker, Bull. Am. Math. Soc. 17, 37-91 (1987).
100. L. Lehner and O. Reula, Status quo and open problems in the numerical construction of space-times, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P. T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
101. E. Lifshitz and I. Khalatnikov, Adv. in Phys. 12, 525-573 (1963).
102. H. Lindblad and I. Rodnianski, Global existence for the Einstein vacuum equations in wave coordinates. arXiv:math.AP/0312479.
103. H. Lindblad and I. Rodnianski, The global stability of Minkowski space-time in harmonic gauge. arXiv:math.AP/0411109.
104. D. Maxwell, Commun. Math. Phys. (2004).
105. D. Maxwell, J. Hyp. Diff. Equ. 2, 521-546 (2005).
106. C. Misner, Phys. Rev. Lett. 29, 1071-1074 (1969).
107. V. Moncrief, Ann. Phys. 132, 87-107 (1981).
108. V. Moncrief and D. Eardley, Gen. Rel. Grav. 13, 887-892 (1981).
109. A. Ori, Phys. Rev. D 61, 024001 (1999).
110. A. Pais, Subtle is the Lord (Oxford University Press, 1982).
111. R. Penrose, Phys. Rev. Lett. 10, 66-68 (1963).
112. R. Penrose, Phys. Rev. Lett. 14, 57-59 (1965).
113. R. Penrose, Rev. Nuovo Cimento 1, 252-276 (1969).
114. R. Penrose, Ann. N.Y. Acad. Sci. 224, 125-134 (1973).
115. R. Penrose, Singularities and time-asymmetry, in: General relativity. An Einstein centenary survey, edited by S. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979).
116. E. Poisson and W. Israel, Phys. Rev. D 41, 1796-1809 (1990).
117. R. Pound and G. Rebka, Phys. Rev. Lett. 4, 337-341 (1960).
118. F. Pretorius, Class. Quantum Gravity 22, 425-451 (2005).
119. R. Price, Phys. Rev. D 5, 2419-2438 (1972).
120. M. Rees, Black holes in the real universe and their prospects as probes of relativistic gravity, in: The Future of Theoretical Physics and Cosmology, edited by G. Gibbons, E. Shellard, and S. Rankin (Cambridge University Press, Cambridge, 2003).
121. A. Rendall, Class. Quantum Gravity 14, 2341-2356 (1997).
122. A. Rendall, Theorems on Existence and Global Dynamics for the Einstein Equations. Living Reviews in Relativity (2002). http://www.livingreviews.org/lrr-2002-6.
123. A. Rendall, Asymptotics of solutions of the Einstein equations with positive cosmological constant, gr-qc/0312020.
124. A. Rendall, The Einstein-Vlasov system, in: The Einstein equations and the large scale behaviour of gravitational fields, edited by P.T. Chruściel and H. Friedrich (Birkhäuser, Basel, 2004).
125. A. Rendall, Class. Quantum Gravity 21, S295-S304 (2004).
126. A. Rendall and M. Weaver, Class. Quantum Gravity 18, 2959-2975 (2001).
127. O. Reula and O. Sarbach, J. Hyp. Diff. Equ. 2, 397-435 (2005).
128. H. Ringström, Class. Quantum Gravity 17, 713-731 (2000);
129. Ann. Inst. Henri Poincare 2, 405-500 (2000);
130. Class. Quantum Gravity 20, 1943-1989 (2003).
131. H. Ringström, J. Hyp. Diff. Equ. 2, 547-564 (2005).
132. O. Sarbach and M. Tiglio, J. Hyp. Diff. Equ. (to appear).
133. R. Schoen, J. Diff. Geom. 20, 479-495 (1984).
134. R. Schoen and S.-T. Yau, Commun. Math. Phys. 79, 231-260 (1981).
135. J. Smoller, A. Wasserman, S.-T. Yau, and J. McLeod, Commun. Math. Phys. 143, 115-147 (1991).
136. K. Stellmacher, Math. Ann. 115, 136-152 (1938).
137. L. Szabados, Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article. Living Reviews in Relativity (2004). http://www.livingreviews.org/lrr-2004-4.
138. D. Tataru, Nonlinear wave equations, in: Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. III, pp. 209-220. (Higher Ed. Press, Beijing, 2002).
139. K. Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy (Norton, New York, 1994).
140. J. Valiente Kroon, Commun. Math. Phys. 251, 211-234 (2004).
141. J. Valiente Kroon, Class. Quantum Gravity 22, 1683-1707 (2005).
142. J. Wainwright and L. Hsu, Class. Quantum Gravity 6, 1409-1431 (1989).
143. R. M. Wald, Gravitational collapse and cosmic censorship, in: Black Holes, Gravitational Radiation and the Universe, edited by B.R. Iyer and B. Bhawal (Dordrecht, Kluwer Academic Publishers, 1999).
144. J. Weisberg and J. Taylor, Relativistic Binary Pulsar B1913+16: Thirty Years of Observation and Analysis. Binary Radio Pulsars. ASP Conference Series, Vol. TBD, 2004, edited by F.A. Rasio and I.H. Stairs (arXiv:astro-ph/0407149).
145. E. Witten, Commun. Math. Phys. 80, 381-402 (1981).
146. G. Yoneda and H. Shinkai, Class. Quantum Gravity 20, L31-L36 (2003).