Abstract
General relativity predicts its own demise at singularities but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were ultimately satisfied, spacetime singularities, although present, would not pose any practical problems to predictability. Here, we argue that under semiclassical effects, the situation should be rather different: the potential singularities which could appear in the theory will generically affect predictability, and so one will be forced to analyse whether there is a way to regularise them. For these possible regularisations, the presence and behaviour of matter during gravitational collapse and stabilisation into new structures will play a key role. First, we show that the static semiclassical counterparts to the Schwarzschild and Reissner–Nordström geometries have singularities which are no longer hidden behind horizons. Then, we argue that in dynamical scenarios of formation and evaporation of black holes, we are left with only three possible outcomes which could avoid singularities and eventual predictability issues. We briefly analyse the viability of each one of them within semiclassical gravity and discuss the expected characteristic timescales of their evolution.
Highlights
A great majority of physicists would agree that classical general relativity (GR) is not completely satisfactory, if only for the fact that it includes situations in which it breaks down: under mild conditions, spacetime singularities are predicted to appear evolving from regular initial conditions [1]
Regularisation of the Polyakov Renormalised Stress-Energy Tensor (RSET) is necessary whenever r = 0 and the region around it are part of the geometry under analysis, as the pathologies at the radial origin can even propagate to other regions of the spacetime. These aspects can sometimes be disregarded when analysing parts of static or dynamical configurations which do not explore the vicinity of r = 0. With this scheme it is possible to obtain an analytical approximation to the RSET which satisfies all the necessary requirements for it to be used as a source term in semiclassical gravity
The available evidence strongly suggests that the new states of equilibrium should be ultracompact stars with no horizons
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It is interesting to note that the static extensions of individual black hole spacetimes one often uses (see, e.g., Kruskal’s maximal extension of the eternal Schwarzschild solution [15]) are examples of Wheeler’s dictum “mass without mass” [16]: all their Cauchy hypersurfaces are devoid of matter These classical GR insights can lead us to believe that (i) the objects resulting from gravitational collapse can be understood to a large extent independently of the behaviour and nature of the matter content (provided it satisfy the appropriate energy conditions) and that (ii) problems with predictability are avoided due to the nature of the gravitational singularities. We will explain how adding semiclassical effects works against the previous reasoning, leading to the opposite conclusions
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