Catastrophic fate of Schwarzschild black holes in a thermal bath

TL;DR

This paper explores the instability of Schwarzschild black holes in thermal baths, revealing that their mass tends to diverge or vanish in finite time, with implications for cosmological models and extra-dimensional theories.

Contribution

It provides a detailed analysis of black hole instability in varying thermal environments, extending previous models and considering extra dimensions and cosmological backgrounds.

Findings

Black hole mass diverges or vanishes in finite time in a thermal bath.

Instability occurs before the background singularity in contracting universes.

Results are consistent across models with extra dimensions.

Abstract

Using the Schwarzschild metric as a rudimentary toy model, we pedagogically revisit the curious prediction that the mass of a classical black hole in a constant temperature thermal bath diverges in a finite amount of time. We study in detail how this instability behaves if the temperature of the bath is allowed to vary with time and conclude that whatever the background behavior (but for a zero-measure subspace of the initial conditions), the black hole mass either diverges or vanishes in a finite time if the Hawking radiation is taken into account. The competition between both effects is subtle and not entirely governed by the hierarchy of the relevant temperatures. This instability is also shown to be reached before the background singularity in a contracting universe, which has implications for bouncing models. The results are generalized to spaces with extra dimensions and the main conclusions are shown to remain true. The limitations of the model are reviewed, both from the point of view of the dynamical black hole horizon and from the point of view of the background space expansion. Comparisons with other approaches are suggested and possible developments are underlined.