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What is a shell-crossing singularity?

Published online by Cambridge University Press:  17 February 2009

Peter Szekeres  and
Anthony Lun
Peter Szekeres
Affiliation:
Department of Physics and Mathematical Physics, University of Adelaide, Adelaide SA 5005, Australia.
Anthony Lun
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
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Abstract

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A detailed discussion of Newtonian and general relativistic spherically symmetric dust solutions leads to the following suggested criteria for a singularity to be classified as a shell-cross: (1) All Jacobi fields have finite limits (in an orthonormal parallel propagated frame) as they approach the singularity. (2) The boundary region forms an essential C2 singularity which is C1 regular, that is it can be transformed away by a C1 coordinate transformation.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 2 , October 1999 , pp. 167 - 179
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bondi, H., Mon. Not. Roy Astron. Soc. 107 (1947) 410.CrossRefGoogle Scholar
[2]Geroch, R. and Horowitz, G. T., in General Relativity: an Einstein Centenary Survey (eds. Hawking, S. W. and Israel, W.), (Cambridge University Press, 1979) 212.Google Scholar
[3]Newman, E. T. and Penrose, R., “An approach to gravitational radiation by a method of spin coefficients”, J. Math. Phys. 3 (1962) 566–578.CrossRefGoogle Scholar
[4]Papapetrou, A. and Hamoui, A., “Couches simples de matière en relativité générale”, Ann. Inst. H. Poincaré 9 (1968) 179–211.Google Scholar
[5]Penrose, R., in General Relativity: an Einstein Centenary Survey (eds. Hawking, S. W. and Israel, W.), (Cambridge University Press, 1979) 581.Google Scholar
[6]Scott, S. M. and Szekeres, P., “The abstract boundary – a new approach to singularities and manifolds”, J. Geom. Phys. 13 (1994) 223–253.CrossRefGoogle Scholar
[7]Szekeres, P., “Global description of spherical collapsing and expanding dust clouds”, Il Nuovo Cimento 17B (1973) 187–195.CrossRefGoogle Scholar
[8]Szekeres, P., “Quasispherical gravitational collapse”, Phys. Rev. D12 (1975) 2941–2948.Google Scholar
[9]Szekeres, P., in A Random Walk in Relativity and Cosmology: Essays in honour of P. C. Vaidya and A. K. Raychaudhuri (eds. Dadhich, N., Krishna Rao, J., Narlikar, J. V. and Vishveshvara, C. V.), (Wiley Eastern Ltd, New Delhi, 1985) 211.Google Scholar
[10]Szekeres, P. and Iyer, V., “Spherically symmetric singularities and strong cosmic censorship”, Phys. Rev. D47 (1993) 4362–4371.Google ScholarPubMed
[11]Tolman, R. C., Proc. Nat. Acad. Sci. USA 20 (1934) 169.CrossRefGoogle Scholar
[12]Yodzis, P., Seifert, H.-J. and Müller Zum Hagen, H., “On the occurrence of naked singularities in general relativity”, Commun. Math. Phys 34 (1973) 135–148.CrossRefGoogle Scholar