The interior of charged black holes and the problem of uniqueness in general relativity. (English) Zbl 1071.83037
The author establishes some results similar to those obtained in M. Dafermos, ”Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations” [Ann. Math. (2) 158, No. 3, 875–928 (2003; Zbl 1055.83002)]. The results are established for data satisfying a weak form of the conjectured Price law decay. The main results are presented in theorems 1.1, 1.2 whose formulations are quite technical. One shows that the heuristic mass inflation scenario put forth by Israel and Poisson is mathematically correct in the context of the considered initial value problem. The maximal future development has a future boundary over which the space-time is extendible as a \(C^0\) metric but along which the Hawking mass blows up identically (hence the space-time is inextendible as a \(C^1\) metric).
Reviewer: Vasile Oproiu (Iaşi)
Citations:
Zbl 1055.83002References:
| [1] | Barack, Phys Rev D (3) 59 pp 17– (1999) |
| [2] | Barack, Phys Rev Lett 82 pp 4388– (1999) |
| [3] | Bi?ák, Gen Relativity Gravitation 3 pp 331– (1972) |
| [4] | Bonanno, Proc Roy Soc London Ser A 450 pp 553– (1995) |
| [5] | Brady, Phys Rev Lett 75 pp 1256– (1995) |
| [6] | Burko, Phys Rev Lett 79 pp 4958– (1997) |
| [7] | Burko, Phys Rev Lett 90 pp 4– (2003) |
| [8] | Burko, Phys Rev D 56 pp 7820– (1997) |
| [9] | Chandrasekhar, Proc Roy Soc London Ser A 384 pp 301– (1982) |
| [10] | Ching, Phys Rev D (3) 52 pp 2118– (1995) |
| [11] | Choquet-Bruhat, Comm Math Phys 14 pp 329– (1969) |
| [12] | Christodoulou, Comm Math Phys 105 pp 337– (1986) |
| [13] | Christodoulou, Comm Math Phys 109 pp 613– (1987) |
| [14] | Christodoulou, Comm Pure Appl Math 44 pp 339– (1991) |
| [15] | Christodoulou, Comm Pure Appl Math 46 pp 1131– (1993) |
| [16] | Christodoulou, Arch Rational Mech Anal 130 pp 343– (1995) |
| [17] | Christodoulou, Ann of Math (2) 149 pp 183– (1999) |
| [18] | Christodoulou, Classical Quantum Gravity 16 pp a23– (1999) |
| [19] | On uniqueness in the large of solutions of Einstein’s equations (?strong cosmic censorship?). Proceedings of the Centre for Mathematics and Its Applications, Australian National University, 27. Australian National University, Centre for Mathematics and Its Applications, Canberra, 1991. · Zbl 0747.53050 |
| [20] | The analysis of space-time singularities. Cambridge Lecture Notes in Physics, 1. Cambridge University Press, Cambridge, 1993. |
| [21] | Dafermos, Ann of Math (2) 158 pp 875– (2003) |
| [22] | Spherically symmetric spacetimes with a trapped surface. Preprint, 2004. |
| [23] | Dafermos, Contemp Math 350 pp 99– (2004) · doi:10.1090/conm/350/06340 |
| [24] | ; A proof of Price’s law for the collapse of a self-gravitating scalar field. Preprint, 2003. Available online at http://www.arxiv.org/abs/gr-qc/0309115. |
| [25] | Friedrich, Comm Math Phys 204 pp 691– (1999) |
| [26] | Gundlach, Phys Rev D 49 pp 883– (1994) |
| [27] | Gundlach, Phys Rev D 49 pp 890– (1994) |
| [28] | ; The large scale structure of space-time. Cambridge Monographs on Mathematical Physics, 1. Cambridge University, London?New York, 1973. · Zbl 0265.53054 · doi:10.1017/CBO9780511524646 |
| [29] | ; Decay of solutions to the wave equation on a spherically symmetric background. Preprint. |
| [30] | Marsa, Phys Rev D (3) 54 pp 4929– (1996) |
| [31] | Ori, Gen Relativity Gravitation 29 pp 881– (1997) |
| [32] | Poisson, Phys Rev D (3) 41 pp 1796– (1990) |
| [33] | Price, Phys Rev D (3) 5 pp 2419– (1972) |
| [34] | Simpson, Internat J Theoret Phys 7 pp 183– (1973) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
