Appearance of the central singularity in spherical collapse

Abstract

We analyze here the structure of non-radial nonspacelike geodesics terminating in the past at a naked singularity formed as the end state of inhomogeneous dust collapse. The spectrum of outgoing nonspacelike null geodesics is examined analytically. The local and global visibility of the singularity is also examined by integrating numerically the null geodesics equations. The possible implications of existence of such families towards the appearance of the star in late stages of gravitational collapse are considered. It is seen that the outgoing non-radial geodesics give an appearance to the naked central singularity as that of an expanding ball whose radius reaches a maximum before the star goes within its apparent horizon. The radiated energy (along the null geodesics) is shown to decay very sharply in the neighbourhood of the singularity. Thus the total energy escaping via non-radial null geodesics from the naked central singularity vanishes in the scenario considered here.Comment: 25 pages, 6 figure

Can We See Naked Singularities?

“…We conclude this by showing that at the most, along one singular geodesic the redshift remains finite, while along all other (infinite family of) singular geodesics the redshift diverges. Earlier Deshingkar et al [6] had shown a similar result for the Tolman-Bondi-Lemaître (TBL) dust model. For the null singularities, this gives a strong evidence in support of CCC, as even though geodesics come out from the singularity we will not be able to see them as no energy or information will reach an observer from such a singularity.…”

“…(9) we see that along the larger root w(r) does not go to zero as r goes to zero and there is only one geodesic coming out of this direction. While along smaller root w(r) = De that at the central singularity K t remains finite along the larger root and it blows up as a negative exponential power of r along the smaller root direction [6]. This exponential divergence is not very surprising as these geodesic stay very close to apparent horizon near the center.…”

“…Though we have studied only ORNGs, the result can be easily generalized for nonradial null as well as timelike geodesics as seen for the TBL models earlier [6,7,8] and we will get K t blowing up when a family of geodesics comes out.…”

“…Proving or disproving CCC is one of the most important open problems in general relativity and black hole physics. There are many specific examples of naked singularities as well as many cases directly or indirectly supporting the conjecture [3,4,5,6,7,8,9,10,11,12,13,14,15]. Most of these studies are based on showing the existence of the outgoing radial null geodesics (ORNGs) from the singularity.…”

“…Our assumptions are most natural and typically we want them to hold for any physically relevant case. All the earlier known cases [3,4,5,6,7,8,9,10,11,12,13,14] of naked singularities in spherically symmetric gravitational collapse of type I matter field fall under our analysis. Our result is based only on local analysis of some Einstein equations and geodesic equations near the central singularity.…”