Comparing Quantum Black Holes and Naked Singularities

There are models of gravitational collapse in classical general relativity which admit the formation of naked singularities as well as black holes. These include fluid models as well as models with scalar fields as matter. Even if fluid models were to be regarded as unphysical in their matter content, the remaining class of models (based on scalar fields) generically admit the formation of visible regions of finite but arbitrarily high curvature. Hence it is of interest to ask, from the point of view of astrophysics, as to what a stellar collapse leading to a naked singularity (or to a visible region of very high curvature) will look like, to a far away observer. The emission of energy during such a process may be divided into three phases (i) the classical phase, during which matter and gravity can both be treated according to the laws of classical physics, (ii) the semiclassical phase, when gravity is treated classically but matter behaves as a quantum field, and (iii) the quantum gravitational phase. In this review, we first give a summary of the status of naked singularities in classical relativity, and then report some recent results comparing the semiclassical phase of black holes with the semiclassical phase of spherical collapse leading to a naked singularity. In particular, we ask how the quantum particle creation during the collapse leading to a naked singularity compares with the Hawking radiation from a star collapsing to form a black hole. It turns out that there is a fundamental difference between the two cases. A spherical naked star emits only about one Planck energy during its semiclassical phase, and the further evolution can only be determined by the laws of quantum gravity. This contrasts with the semiclassical evaporation of a black hole wherein gravity can be treated classically all the way till the final stages of evaporation until a Planck mass remnant remains. Hence spherical collapse leading to a naked singularity provides an interesting and promising system for testing our understanding of quantum gravity. The results on the semiclassical phase of naked collapse reviewed here have been obtained in collaboration with Barve, Harada, Iguchi, Nakao, Tanaka, Vaz and Witten 1 Cosmic Censorship and Classical General Relativity Put in broad physical terms, the Cosmic Censorship Hypothesis states that generic gravitational collapse of physically reasonable matter does not end in the formation of a naked singularity. A naked singularity is a singularity which is visible to a far away observer, i.e. outgoing light rays starting from the singularity terminate on the singularity in the past. By ‘physically reasonable’ we mean matter which satisfies one or more positive energy conditions matter which can in principle be prepared in the laboratory. By ‘generic’ we mean that the initial conditions leading to the formation of the naked singularity are not special (of zero measure). The Censorship Hypothesis is important in classical general relativity because there are theorems, for instance the black hole area theorem, whose proof assumes the validity of the Hypothesis. However, it is not obvious a priori that the results of these theorems cannot be proved without assuming Censorship. This by itself is an interesting direction for research in the classical theory. The issue of naked singularities is not trivialized by quantum gravity, even though it might be true that quantum gravity will remove the singularities of classical general relativity, by replacing them by a smeared out region of Planck scale curvature. If the classical singularity resides inside an astrophysical black hole, Based on a talk given at JGRG10, Osaka, September, 2000. To appear in the conference proceedings.