Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse

Abstract

We investigate here the occurrence and nature of naked singularity for the inhomogeneous gravitational collapse of Tolman-Bondi dust clouds. It is shown that the naked singularities form at the center of the collapsing cloud in a wide class of collapse models which includes the earlier cases considered by Eardley and Smarr [5] and Christodoulou [6]. This class also contains self-similar as well as non-self-similar models. The structure and strength of this singularity is examined and the question is investigated as to when a non-zero measure set of non-spacelike trajectories could be emitted from the singularity as opposed to isolated trajectories coming out. It is seen that the weak energy condition and positivity of energy density ensures that the families of non-spacelike trajectories come out of the singularity. The curvature strength of the naked singularity is examined which provides an important test for its physical significance. This is done in terms of the strong curvature condition which ensures that all the volume forms must be crushed to zero size in the limit of approach to the singularity; and also the divergence of the Kretschmann scalar K = R abcd R abcd is pointed out. We show that the class considered here contains sub-classes of solutions which admit strong curvature naked singularities in either of the senses stated above. The conditions are discussed for the naked singularity to be globally naked. An implication for the fundamental issue of the final fate of gravitational collapse is that naked singularities need not be considered as artifacts of geometric symmetries of space-time such as self-similarity, but arise in a wide range of gravitational collapse scenarios once the inhomogeneities in the matter distribution are taken into account. It is argued that a physical formulation for the cosmic censorship may be evolved which avoids the features above. Possibilities in this direction are suggested while indicating that the analysis presented here should 2 be useful for any possible rigorous formulation of the cosmic censorship hypothesis.3

Power, energy, and spectrum of a naked singularity explosion

“…Detailed analysis on the occurrence of naked shell-focusing singularity has been done in [1][2][3][4][29][30][31]. Here we present one of the results.…”

“…It was shown that the collapse of an inhomogeneous dust ball results in shell-focusing naked singularity formation [1][2][3][4]. Ori and Piran [5][6][7] and Harada [8] showed that naked singularity formation is possible from the spherical collapse of a perfect fluid with a very soft equation of state.…”

Quantum vacuum effects on the final fate of a collapsing ball of dust

“…This causes the shrinkage of the collapsing object due to the radiation of high energy matter fluxes. Such effects are claimed to result from the formation of naked singularities [13]. These secondary effects and similar ones are considered to provide probable empirical evidences for the indirect proof of some quantum gravity theories [1].…”

Scalar field collapse with an exponential potential

“…Gravitational collapse is well studied analytically and numerically, in the framework of General Relativity [6,7,8,9,10,11], and modifications of GR as well [12,13,14,15,16,17]. The exact solution of Einsteins' field equations play a crucial role in understanding a collapsing solution in a detailed manner.…”