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Volumn 16, Issue 8, 1999, Pages

On local and global aspects of the Cauchy problem in general relativity

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EID: 0033460737     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/16/8/201     Document Type: Review
Times cited : (53)

References (73)
  • 2
    • 0003796630 scopus 로고
    • New York: Academic
    • Adams 1975 Sobolev Spaces (New York: Academic)
    • (1975) Sobolev Spaces
    • Adams1
  • 3
    • 0037777456 scopus 로고
    • Propagation de l'analiticité des solutions de systèmes hyperboliques non-linéaires
    • Alhinac S and Métivier G 1984 Propagation de l'analiticité des solutions de systèmes hyperboliques non-linéaires Invent. Math. 75 189-204
    • (1984) Invent. Math. , vol.75 , pp. 189-204
    • Alhinac, S.1    Métivier, G.2
  • 4
    • 0000423572 scopus 로고    scopus 로고
    • Appearance of coordinate shocks in hyperbolic formalisms of general relativity
    • Alcubierre M 1997 Appearance of coordinate shocks in hyperbolic formalisms of general relativity Phys. Rev. D 55 5981-91
    • (1997) Phys. Rev. D , vol.55 , pp. 5981-5991
    • Alcubierre, M.1
  • 5
    • 0001074658 scopus 로고    scopus 로고
    • Pathologies of hyperbolic gauges in general relativity and other field theories
    • Alcubierre M and Massó J 1998 Pathologies of hyperbolic gauges in general relativity and other field theories Phys. Rev. D 57 R4511-5
    • (1998) Phys. Rev. D , vol.57
    • Alcubierre, M.1    Massó, J.2
  • 6
    • 34249839460 scopus 로고
    • On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for the Einstein's field equations
    • Andersson L, Chrúsciel P T and Friedrich H 1992 On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for the Einstein's field equations Commun. Math. Phys. 149 587-612
    • (1992) Commun. Math. Phys. , vol.149 , pp. 587-612
    • Andersson, L.1    Chrúsciel, P.T.2    Friedrich, H.3
  • 7
    • 0013198965 scopus 로고    scopus 로고
    • Solutions of the constraint equations in general relativity satisfying hyperboloidal boundary conditions
    • Polska Academic Nauk
    • Andersson L and Chrúsciel P T 1996 Solutions of the constraint equations in general relativity satisfying hyperboloidal boundary conditions Dissertationes Mathematicae (Polska Academic Nauk)
    • (1996) Dissertationes Mathematicae
    • Andersson, L.1    Chrúsciel, P.T.2
  • 8
    • 85049057407 scopus 로고    scopus 로고
    • On the global evolution problem in 3 + 1 gravity
    • in preparation
    • Andersson L and Moncrief V On the global evolution problem in 3 + 1 gravity J. Geom. Phys. in preparation
    • J. Geom. Phys.
    • Andersson, L.1    Moncrief, V.2
  • 9
    • 0031280684 scopus 로고    scopus 로고
    • On the global existence problem in 2 + 1 gravity
    • Andersson L, Moncrief V and Tromba A J 1997 On the global existence problem in 2 + 1 gravity J. Geom. Phys. 23 191-205
    • (1997) J. Geom. Phys. , vol.23 , pp. 191-205
    • Andersson, L.1    Moncrief, V.2    Tromba, A.J.3
  • 10
    • 0000177308 scopus 로고
    • Coordinate invariance and energy expressions in general relativity
    • Arnowitt R, Deser S and Misner C 1961 Coordinate invariance and energy expressions in general relativity Phys. Rev. 122 997-1006
    • (1961) Phys. Rev. , vol.122 , pp. 997-1006
    • Arnowitt, R.1    Deser, S.2    Misner, C.3
  • 11
    • 0000624702 scopus 로고
    • Existence of maximal surfaces in asymptotically flat space-times
    • Bartnik R 1984 Existence of maximal surfaces in asymptotically flat space-times Commun. Math. Phys. 94 155-75
    • (1984) Commun. Math. Phys. , vol.94 , pp. 155-175
    • Bartnik, R.1
  • 12
    • 0000902792 scopus 로고
    • Introduction d'un tenseur du quatrieme ordre
    • Bel L 1959 Introduction d'un tenseur du quatrieme ordre C. R. Acad. Sci., Paris 247 1094-6
    • (1959) C. R. Acad. Sci., Paris , vol.247 , pp. 1094-1096
    • Bel, L.1
  • 14
    • 0001505323 scopus 로고
    • Numerical investigation of cosmological singularities
    • Berger B K and Moncrief V 1993 Numerical investigation of cosmological singularities Phys. Rev. D 48 4676-87
    • (1993) Phys. Rev. D , vol.48 , pp. 4676-4687
    • Berger, B.K.1    Moncrief, V.2
  • 15
    • 25544468506 scopus 로고
    • Hereditary effects in gravitational radiation
    • Blanchet L and Damour T 1992 Hereditary effects in gravitational radiation Phys. Rev. D 46 4304-19
    • (1992) Phys. Rev. D , vol.46 , pp. 4304-4319
    • Blanchet, L.1    Damour, T.2
  • 16
    • 0002022619 scopus 로고
    • Isolated maximal surfaces in spacetime
    • Brill D and Flaherty F 1976 Isolated maximal surfaces in spacetime Commun. Math. Phys. 50 157-65
    • (1976) Commun. Math. Phys. , vol.50 , pp. 157-165
    • Brill, D.1    Flaherty, F.2
  • 17
    • 34250590049 scopus 로고
    • Théorème d existence pour certain systèmes d'equations aux dérivées partielles nonlinéaires
    • Choquet-Bruhat Y 1952 Théorème d existence pour certain systèmes d'equations aux dérivées partielles nonlinéaires Act. Math. 88 141-225
    • (1952) Act. Math. , vol.88 , pp. 141-225
    • Choquet-Bruhat, Y.1
  • 19
    • 0347112949 scopus 로고
    • Un théorème d'instabilité pour certain équations hyperboliques nonlinéaires
    • Choquet-Bruhat Y 1973 Un théorème d'instabilité pour certain équations hyperboliques nonlinéaires C. R. Acad. Sci., Paris A 276 281
    • (1973) C. R. Acad. Sci., Paris A , vol.276 , pp. 281
    • Choquet-Bruhat, Y.1
  • 20
    • 0001127920 scopus 로고
    • Existence of global solutions of the Yang-Mills, Higgs and spinor fields in 3 + 1 dimensions
    • Choquet-Bruhat Y and Christodoulou D 1981 Existence of global solutions of the Yang-Mills, Higgs and spinor fields in 3 + 1 dimensions Annales des Ecole Normale Sup. 4th series vol 14 pp 481-506
    • (1981) Annales des Ecole Normale Sup. 4th Series , vol.14 , pp. 481-506
    • Choquet-Bruhat, Y.1    Christodoulou, D.2
  • 22
    • 34250590049 scopus 로고
    • Un théorème d'existence pour certain systèmes d'equations aux derivées partielles non linéaires
    • Choquet-Bruhat Y and Fourès Y 1952 Un théorème d'existence pour certain systèmes d'equations aux derivées partielles non linéaires Act. Math. 88 141-225
    • (1952) Act. Math. , vol.88 , pp. 141-225
    • Choquet-Bruhat, Y.1    Fourès, Y.2
  • 23
    • 0000307876 scopus 로고
    • Global aspects of the Cauchy problem in general relativity
    • Choquet-Bruhat Y and Geroch R P 1969 Global aspects of the Cauchy problem in general relativity Commun. Math. Phys. 14 329-35
    • (1969) Commun. Math. Phys. , vol.14 , pp. 329-335
    • Choquet-Bruhat, Y.1    Geroch, R.P.2
  • 24
    • 33845641932 scopus 로고
    • Hyperbolicity of the 3+1 system of Einstein equations
    • Choquet-Bruhat Y and Ruggeri T 1983 Hyperbolicity of the 3+1 system of Einstein equations Commun. Math. Phys. 89 269-75
    • (1983) Commun. Math. Phys. , vol.89 , pp. 269-275
    • Choquet-Bruhat, Y.1    Ruggeri, T.2
  • 26
    • 18544385583 scopus 로고
    • A mathematical theory of gravitational collapse
    • Christodoulou D 1987 A mathematical theory of gravitational collapse Commun. Math. Phys. 109 613-47
    • (1987) Commun. Math. Phys. , vol.109 , pp. 613-647
    • Christodoulou, D.1
  • 27
    • 0042344382 scopus 로고
    • Solutions globales des equations de champ de Yang-Mills
    • Christodoulou D 1981 Solutions globales des equations de champ de Yang-Mills C. R. Acad. Sci., Paris A 293 39-42
    • (1981) C. R. Acad. Sci., Paris A , vol.293 , pp. 39-42
    • Christodoulou, D.1
  • 28
    • 84990602498 scopus 로고
    • Global solutions for nonlinear hyperbolic equations for small data
    • Christodoulou D 1986 Global solutions for nonlinear hyperbolic equations for small data Commun. Pure Appl. Math. 39 267-82
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 29
    • 84990591638 scopus 로고
    • Asymptotic properties of linear field equations in Minkowski space
    • Christodoulou D and Klainerman S 1990 Asymptotic properties of linear field equations in Minkowski space Commun. Pure Appl. Math. XLIII 137-99
    • (1990) Commun. Pure Appl. Math. , vol.43 , pp. 137-199
    • Christodoulou, D.1    Klainerman, S.2
  • 33
    • 4244075062 scopus 로고
    • On the uniqueness in the large of solutions to the Einstein equations (strong cosmic censorship)
    • Providence, RI: American Mathematical Society
    • Chrúsciel P T 1992 On the uniqueness in the large of solutions to the Einstein equations (strong cosmic censorship) Mathematical Aspects of Classical Field Theory (Seattle, WA 1991) (Providence, RI: American Mathematical Society) pp 235-73
    • (1992) Mathematical Aspects of Classical Field Theory (Seattle, WA 1991) , pp. 235-273
    • Chrúsciel, P.T.1
  • 34
    • 33846122549 scopus 로고
    • The global existence problem and cosmic censorship in general relativity
    • Eardley D and Moncrief V 1981 The global existence problem and cosmic censorship in general relativity Gen. Rel. Grav. 13 887-92
    • (1981) Gen. Rel. Grav. , vol.13 , pp. 887-892
    • Eardley, D.1    Moncrief, V.2
  • 35
    • 0003054750 scopus 로고
    • The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I
    • Fisher A and Marsden J E 1972 The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I Commun. Math. Phys. 28 1-38
    • (1972) Commun. Math. Phys. , vol.28 , pp. 1-38
    • Fisher, A.1    Marsden, J.E.2
  • 36
    • 0347112946 scopus 로고
    • General relativity, partial differential equations and dynamical systems
    • Fisher A and Marsden J E 1973 General relativity, partial differential equations and dynamical systems AMS Proc. Symp. Pure Math. 23 309-27
    • (1973) AMS Proc. Symp. Pure Math. , vol.23 , pp. 309-327
    • Fisher, A.1    Marsden, J.E.2
  • 37
    • 0001155750 scopus 로고
    • Cauchy problems for the conformal vacuum field equations in general relativity
    • Friedrich H 1983 Cauchy problems for the conformal vacuum field equations in general relativity Commun. Math. Phys. 91 445-72
    • (1983) Commun. Math. Phys. , vol.91 , pp. 445-472
    • Friedrich, H.1
  • 38
    • 0011467717 scopus 로고
    • Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant
    • Friedrich H 1986 Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant J. Geom. Phys. 3 101-17
    • (1986) J. Geom. Phys. , vol.3 , pp. 101-117
    • Friedrich, H.1
  • 39
    • 84972497586 scopus 로고
    • On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations
    • Friedrich H 1991 On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations J. Differ. Geom. 34 275-345
    • (1991) J. Differ. Geom. , vol.34 , pp. 275-345
    • Friedrich, H.1
  • 40
    • 22244445878 scopus 로고    scopus 로고
    • Hyperbolic reductions for Einstein equations
    • Friedrich H 1996 Hyperbolic reductions for Einstein equations Class. Quantum Grav. 13 1451-69
    • (1996) Class. Quantum Grav. , vol.13 , pp. 1451-1469
    • Friedrich, H.1
  • 42
    • 34047263340 scopus 로고
    • The domain of dependence
    • Geroch R P 1970 The domain of dependence J. Math. Phys. 11 437-9
    • (1970) J. Math. Phys. , vol.11 , pp. 437-439
    • Geroch, R.P.1
  • 43
    • 0001301252 scopus 로고
    • H-surfaces in Lorentzian manifolds
    • Gerhardt C 1983 H-surfaces in Lorentzian manifolds Commun. Math. Phys. 89 523-53
    • (1983) Commun. Math. Phys. , vol.89 , pp. 523-553
    • Gerhardt, C.1
  • 44
    • 0000775061 scopus 로고
    • Gravitational waves in closed universes
    • Gowdy R H 1971 Gravitational waves in closed universes Phys. Rev. Lett. 27 826-9
    • (1971) Phys. Rev. Lett. , vol.27 , pp. 826-829
    • Gowdy, R.H.1
  • 45
    • 0642300596 scopus 로고
    • Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions
    • Gowdy R H 1974 Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: topologies and boundary conditions Ann. Phys. 83 203-41
    • (1974) Ann. Phys. , vol.83 , pp. 203-241
    • Gowdy, R.H.1
  • 46
    • 0007270307 scopus 로고
    • The conservation of matter in general relativity
    • Hawking S W 1970 The conservation of matter in general relativity Commun. Math. Phys. 18 301-6
    • (1970) Commun. Math. Phys. , vol.18 , pp. 301-306
    • Hawking, S.W.1
  • 48
    • 0017428498 scopus 로고
    • Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
    • Hughes T J R, Kato T and Marsden J E 1976 Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity Arch. Rational Mech. Anal. 63 273-94
    • (1976) Arch. Rational Mech. Anal. , vol.63 , pp. 273-294
    • Hughes, T.J.R.1    Kato, T.2    Marsden, J.E.3
  • 49
    • 0030549263 scopus 로고    scopus 로고
    • Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
    • Huisken G and Yau S T 1996 Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature Inventiones Matematicae
    • (1996) Inventiones Matematicae
    • Huisken, G.1    Yau, S.T.2
  • 50
    • 21844481319 scopus 로고
    • Constant mean curvature solutions of the Einstein constraint equations on closed manifolds
    • Isenberg J 1995 Constant mean curvature solutions of the Einstein constraint equations on closed manifolds Class. Quantum Grav. 12 2249-74
    • (1995) Class. Quantum Grav. , vol.12 , pp. 2249-2274
    • Isenberg, J.1
  • 53
    • 0000744112 scopus 로고
    • Linear evolution equation of hyperbolic type
    • Kato T 1970 Linear evolution equation of hyperbolic type J. Fac. Sci. Univ. Tokyo 17 241-58
    • (1970) J. Fac. Sci. Univ. Tokyo , vol.17 , pp. 241-258
    • Kato, T.1
  • 55
    • 0000870142 scopus 로고
    • The null condition and global existence to nonlinear wave equations
    • Klainerman S 1986 The null condition and global existence to nonlinear wave equations Lect. Appl. Math. 23 293-326
    • (1986) Lect. Appl. Math. , vol.23 , pp. 293-326
    • Klainerman, S.1
  • 56
    • 84990556410 scopus 로고
    • Remarks on the global Sobolev inequalities in Minkowski space
    • Klainerman S 1987 Remarks on the global Sobolev inequalities in Minkowski space Commun. Pure Appl. Math. 40 111-7
    • (1987) Commun. Pure Appl. Math. , vol.40 , pp. 111-117
    • Klainerman, S.1
  • 57
    • 84990602599 scopus 로고
    • Uniform decay estimates and the Lorentz invariance of the classical wave equation
    • Klainerman S 1985 Uniform decay estimates and the Lorentz invariance of the classical wave equation Commun. Pure Appl. Math. 38 321-32
    • (1985) Commun. Pure Appl. Math. , vol.38 , pp. 321-332
    • Klainerman, S.1
  • 58
    • 84980074238 scopus 로고
    • Non linear hyperbolic equations
    • Lax P D 1953 Non linear hyperbolic equations Commun. Pure Appl. Math. 6 231-58
    • (1953) Commun. Pure Appl. Math. , vol.6 , pp. 231-258
    • Lax, P.D.1
  • 60
    • 0001763234 scopus 로고
    • New conservation laws for zero rest-mass fields in asymptotically flat space-time
    • Newman E T and Penrose R 1968 New conservation laws for zero rest-mass fields in asymptotically flat space-time Proc. R. Soc. A 305 175-204
    • (1968) Proc. R. Soc. A , vol.305 , pp. 175-204
    • Newman, E.T.1    Penrose, R.2
  • 61
    • 84972536320 scopus 로고
    • An abstract form of the nonlinear Cauchy-Kowaleski theorem
    • Nirenberg L 1972 An abstract form of the nonlinear Cauchy-Kowaleski theorem J. Differ. Geom. 6 561-76
    • (1972) J. Differ. Geom. , vol.6 , pp. 561-576
    • Nirenberg, L.1
  • 62
    • 0003074871 scopus 로고
    • Conformal treatment of infinity
    • ed B deWitt and C deWitt (New York: Gordon and Breach)
    • Penrose R 1963 Conformal treatment of infinity Relativity, Groups and Topology ed B deWitt and C deWitt (New York: Gordon and Breach)
    • (1963) Relativity, Groups and Topology
    • Penrose, R.1
  • 63
    • 0001207885 scopus 로고
    • Zero rest mass fields including gravitation: Asymptotic behavior
    • Penrose R 1962 Zero rest mass fields including gravitation: asymptotic behavior Proc. R. Soc. A 284 159-203
    • (1962) Proc. R. Soc. A , vol.284 , pp. 159-203
    • Penrose, R.1
  • 64
    • 80655126190 scopus 로고    scopus 로고
    • Local and global existence theorems for the Einstein equations
    • Rendall A D 1998 Local and global existence theorems for the Einstein equations Living Rev. Relativity URL: http://www.livingreviews.org/Articles/Volume1/1998-4rendall
    • (1998) Living Rev. Relativity
    • Rendall, A.D.1
  • 65
    • 0005179502 scopus 로고    scopus 로고
    • Existence and non-existence results for global constant mean curvature foliations
    • Rendall A D 1997 Existence and non-existence results for global constant mean curvature foliations Proc: 2nd World Congress of Nonlinear Analysts (Athens, 1996) pt 6, vol 30 pp 3589-98
    • (1997) Proc: 2nd World Congress of Nonlinear Analysts (Athens, 1996) , vol.30 , Issue.6 PART , pp. 3589-3598
    • Rendall, A.D.1
  • 66
    • 21344498199 scopus 로고
    • The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system
    • Rendall A D 1994 The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system Commun. Math. Phys. 163 89-112
    • (1994) Commun. Math. Phys. , vol.163 , pp. 89-112
    • Rendall, A.D.1
  • 67
    • 0347112944 scopus 로고    scopus 로고
    • Hyperbolic methods for the Einstein equations
    • Reula O 1998 Hyperbolic methods for the Einstein equations Living Rev. Relativity URL: http://www.livingreviews.org /Articles/Volume1/1998-3reula
    • (1998) Living Rev. Relativity
    • Reula, O.1
  • 69
    • 33646610527 scopus 로고
    • Kinematical conditions in the construction of spacetime
    • Smarr L and York J 1978 Kinematical conditions in the construction of spacetime Phys. Rev. D 17 2529-51
    • (1978) Phys. Rev. D , vol.17 , pp. 2529-2551
    • Smarr, L.1    York, J.2
  • 70
    • 26744444552 scopus 로고
    • Radiation gauge in general relativity
    • Smarr L and York J 1978 Radiation gauge in general relativity Phys. Rev. D 17 1945-56
    • (1978) Phys. Rev. D , vol.17 , pp. 1945-1956
    • Smarr, L.1    York, J.2
  • 72
    • 0346482749 scopus 로고    scopus 로고
    • Gravitational collapse and cosmic censorship
    • Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068
    • (1997) Preprint Gr-qc/9710068
    • Wald, R.1
  • 73
    • 0002849466 scopus 로고    scopus 로고
    • Recent work connected with the Kakeya problem
    • ed H Rossi (Providence, RI: American Mathematical Society)
    • Wolff T 1998 Recent work connected with the Kakeya problem Prospects in Mathematics ed H Rossi (Providence, RI: American Mathematical Society)
    • (1998) Prospects in Mathematics
    • Wolff, T.1


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