Relativistic shells: Dynamics, horizons, and shell crossing

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 66, Issue 8, 2002, Pages

  Gonçalves, Sérgio M C V ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COSMOLOGICAL PHENOMENA; ENERGY; MASS; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; PRESSURE; TIME; VACUUM;

EID: 18344402060     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.084021     Document Type: Article

References (38)

1. W. Israel, Phys. Rev. 153, 1388 (1967).
2. A. Krasińsky, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, England, 1997).
3. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
4. M. Visser, Phys. Rev. D 39, 3182 (1989).
5. See, e.g., L. Anchordoqui et al., Phys. Rev. D 64, 084027 (2001).
6. N. Sen, Ann. Phys. (Leipzig) 73, 365 (1924).
7. K. Lanczos, Ann. Phys. (Leipzig) 74, 518 (1924).
8. G. Darmois, Mémorial des Sciences Mathématiques (Gauthier-Villars, Paris, France, 1927), Vol. 25.
9. W. Israel, Nuovo Cimento Soc. Ital. Fis., B 44, 1 (1966);
10. Nuovo Cimento Soc. Ital. Fis., BW. Israel48, 463 (1967).
11. C. Barrabès and W. Israel, Phys. Rev. D 43, 1129 (1991).
12. A. Lichnerowicz, Théories Relativistes de la Gravitation et de l’Electromagnetisme (Masson, Paris, France, 1955).
13. K. Lake and P. Musgrave, Class. Quantum Grav. 13, 1885 (1996).
14. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th rev. ed. (Butterworth-Heinemann, Oxford, England, 1999).
15. G. Lemaître, Ann. Soc. R. Sci. Med. Nat. Bruxelles A53, 51 (1933);
16. R.C. Tolman, Proc. Natl. Acad. Sci. U.S.A. 20, 410 (1934);
17. H. Bondi, Mon. Not. R. Astron. Soc. 107, 343 (1948).
18. Misner, Thorne, and Wheeler, Sec. 32.4 of 3.
19. This is the so-called Einstein cluster model, introduced by Einstein himself to probe the effects of rotation in spherical geometries without spoiling the latter symmetry. See A. Einstein, Ann. Math. 40, 922 (1939).
20. M. Visser, Lorentzian Wormholes: From Einstein to Hawking (American Institute of Physics, New York, 1996).
21. R. Penrose, in Batelle Rencountres, edited by C. M. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1968).
22. R. M. Wald, General Relativity (Chicago University Press, Chicago, 1984).
23. D. M. Eardley and L. Smarr, Phys. Rev. D 19, 2239 (1979);
24. D. Christodoulou, Commun. Math. Phys. 93, 171 (1984);
25. R. P. A. C. Newman, Class. Quantum Grav. 3, 527 (1986).
26. P. Yodzis, H. J. Seifert, and H. M. zum Hagen, Commun. Math. Phys. 34, 135 (1973).
27. A. Ori, Phys. Rev. D 44, 2278 (1991).
28. S. M. C. V. Gonçalves, Phys. Rev. D 63, 124017 (2001).
29. Newman 20.
30. A. Papapetrou and A. H. Hamoui, Ann. Inst. Henri Poincare, Sect. A VI, 343 (1967).
31. P. Szekeres and A. Lun, J. Aust. Math. Soc. B, Appl. Math. 41, 167 (1999).
32. T. Dray and G. ’t Hooft, Commun. Math. Phys. 99, 613 (1985);
33. I. H. Redmount, Prog. Theor. Phys. 73, 1401 (1985).
34. D. Núñez, H. P. Oliveira, and J. Salim, Class. Quantum Grav. 10, 1117 (1993).
35. P. R. Brady, J. Louko, and E. Poisson, Phys. Rev. D 44, 1891 (1991);
36. Phys. Rev. Dsee also M. Ishak and K. Lake, 65, 044011 (2002).
37. J. Frauendiener, C. Hoenselaers, and W. Konrad, Class. Quantum Grav. 7, 585 (1990).
38. The upper limit for the initial radius of the outer shell depends on the initial radius for the inner shell, and on both masses (Formula presented)