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Visibility of a spacetime singularity
Phys. Rev. D 75, 044005 – Published 5 February, 2007
DOI: https://doi.org/10.1103/PhysRevD.75.044005
Abstract
We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.
Article Text
References (9)
- S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge 1973).
- R. Goswami, P. S. Joshi, and P. Singh, Phys. Rev. Lett. 96, 031302 (2006). For a possible quantum resolution of the big bang singularity within the loop quantum gravity framework, see e.g. M. Bojowald, Living Rev. Relativity 8, 11 (2005); A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 73, 124038 (2006), and references therein.
- A. Krolak, Prog. Theor. Phys. Suppl. 136, 45 (1999); P. S. Joshi, Pramana 55, 529 (2000); R. Giambo’, F. Giannoni, G. Magli, and P. Piccione, Commun. Math. Phys. 235, 545 (2003); T. Harada, H. Iguchi, and K. Nakao, Prog. Theor. Phys. 107, 449 (2002).
- F. C. Mena and B. Nolan, Classical Quantum Gravity 18, 4531 (2001). 19, 2587 (2002); S. S. Deshingkar and P. S. Joshi, Phys. Rev. D 63, 024007 (2000); S. S. Deshingkar, P. S. Joshi, I. H. Dwivedi, 65, 084009 (2002).
- P. S. Joshi and I. H. Dwivedi, Commun. Math. Phys. 146, 333 (1992); Lett. Math. Phys. 27, 235 (1993); I. H. Dwivedi and P. S. Joshi, Classical Quantum Gravity 6, 1599 (1989); 8, 1339 (1991).
- R. Geroch, E. Kronheimer, and R. Penrose, Proc. R. Soc. A 327, 545 (1972).
A boundary attachment to the spacetime manifold is essential to treat the regular spacetime events together with its singularities and points at infinity in a unified manner. There are different ways to attach a boundary to the spacetime, and they all do not necessarily give the same result. We have used here the approach as given in [6] as it depends basically only on the causal structure of spacetime, which is more fundamental as compared to, for example, the differential structure of the spacetime manifold. Also, from a physical point of view, each ideal point here is directly associated with the region of spacetime which it can influence, or which it would be influenced by.
It is known, e.g. in the case of dust collapse, that once the singularity is locally naked, the choice of a suitable behavior of the mass function (which is a free function, subject only to some physical conditions such as an energy condition and regularity of the initial data) away from the center, allows the null rays to come out from the boundary of the cloud (see [5]). It may also be noted that in certain classes of self-similar collapse, once the singularity is locally naked it becomes necessarily globally visible. In any case, as there is no scale in the problem, once the singularity is locally visible, an observer within a large enough black hole will still be able to see it for a long enough time. In such a scenario, the escape of rays outside the boundary of the cloud would not be crucial.
- R. Giambo’, J. Math. Phys. (N.Y.) 47, 022501 (2006).