Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations

Annals of Mathematics

Volumn 158, Issue 3, 2003, Pages 875-928

  Dafermos, Mihalis ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1442308254     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2003.158.875     Document Type: Article

References (20)

1. A. BONANNO, S. DROZ, W. ISRAEL, and S. M. MORSINK, Structure of the charged spherical black hole interior, Proc. Roy. Soc. London Ser. A 450 (1995), 553-567.
2. P. R. BRADY and J. D. SMITH, Black hole singularities: a numerical approach, Phys. Rev. Lett. 75 (1995), 1256-1259.
3. S. CHANDRASEKHAR and J. B. HARTLE, On crossing the Cauchy horizon of a Reissner-Nordström black-hole, Proc. Roy. Soc. London Ser. A 384 (1982), 301-315.
4. Y. CHOQUET-BRUHAT and R. GEROCH, Global aspects of the Cauchy problem in general relativity, Comm. Math. Phys. 14 (1969), 329-335.
5. D. CHRISTODOULOU, The instability of naked singularities in the gravitational collapse of a scalar field, Ann. of Math. 149 (1999), 183-217.
6. _, On the global initial value problem and the issue of singularities, Classical Quantum Gravity 16 (1999), A23-A35.
7. _, Self-gravitating relativistic fluids: a two-phase model, Arch. Rational Mech. Anal. 130 (1995), 343-400.
8. _, Bounded variation solutions of the spherically symmetric Einstein-scalar field equations, Comm. Pure Appl. Math. 46 (1993), 1131-1220.
9. _, The formation of black holes and singularities in spherically symmetric gravitational collapse, Comm. Pure Appl. Math. 44 (1991), 339-373.
10. _, The problem of a self-gravitating scalar field, Comm. Math. Phys. 105 (1986), 337-361.
11. D. CHRISTODOULOU and S. KLAINERMAN, The Global Nonlinear Stability of the Minkowski Space, Princeton Math. Series 41, Princeton Univ. Press, Princeton, NJ, 1993.
12. P. T. CHRUŚCIEL, On Uniqueness in the Large of Solutions of the Einstein's Equations ("strong cosmic censorship"), Proc. Centre Math. Anal. Austral. Nat. Univ. 27, Australian National University, Canberra, 1991.
13. C. J. S. CLARKE, The Analysis of Space-Time Singularities, Cambridge Lecture Notes in Physics 1, Cambridge Univ. Press, Cambridge, 1993.
14. M. Dafermos, Strong cosmic censorship and the spherically-symmetric Einstein-Maxwell-scalar field equations, Ph.D. Thesis, Princeton University, 2001.
15. S. W. HAWKING and G. F. R. ELLIS, The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, No. 1, Cambridge Univ. Press, New York, 1973.
16. S. KLAINERMAN and I. RODNIANSKI, Rough solutions for the Einstein vacuum equations, Ann. of Math., to appear.
17. R. PENROSE, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57-59.
18. E. POISSON and W. ISRAEL, Internal structure of black holes, Phys. Rev. D 41 (1990), 1796-1809.
19. M. SIMPSON and R. PENROSE, Internal instability in a Reissner-Nordström black hole, Internatl. J. Theor. Phys. 7 (1973), 183-197.
20. S.-T. YAU, Problem section, in Seminar on Differential Geometry (S.-T. Yau, ed.), Ann. of Math. Studies 102, 669-706, Princeton Univ. Press, Princeton, NJ, 1982.