The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity

TL;DR

This paper explores the evolution and stability of Nariai black holes in modified gravity theories, revealing scenarios like instabilities, evaporation, and anti-evaporation, with implications for primordial black holes and the nature of gravity.

Contribution

It provides a comprehensive analysis of Nariai black hole perturbations in both $F(R)$ and Gauss-Bonnet gravity, highlighting conditions for stability and anti-evaporation.

Findings

Rich variety of black hole evolution scenarios in $F(R)$ gravity

Anti-evaporation may occur in certain models, suggesting primordial black holes could indicate modified gravity

Nariai black holes can be stable in some Gauss-Bonnet gravity cases

Abstract

We investigate the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial black holes at current universe may indicate towards the modified gravity which supports the anti-evaporation as preferrable model. As some generalization we extend the study of Nariai black hole evolution to modified Gauss-Bonnet gravity. The corresponding perturbations equations turn out to be much more complicated than in the case of $F(R)$ gravity. For specific example of modified Gauss-Bonnet gravity we demonstrate that Nariai solution maybe stable.