Instabilities and Anti-Evaporation of Reissner-Nordstr\"om Black Holes in modified $F(R)$ gravity

TL;DR

This paper investigates the stability and anti-evaporation phenomena of extremal Reissner-Nordström black holes within $F(R)$ gravity, revealing conditions under which anti-evaporation occurs and deriving related solutions.

Contribution

It demonstrates anti-evaporation effects in $F(R)$ gravity, including cases with electromagnetic fields, and derives general spherically symmetric solutions in the Einstein frame.

Findings

Anti-evaporation occurs in strong coupling limits of $F(R)$ gravity.

Effective electric charge can be generated without electromagnetic fields.

Anti-evaporation is present in Maxwell-$F(R)$ gravity but not in Maxwell-Einstein gravity.

Abstract

We study the instabilities and related anti-evaporation of the extremal Reissner-Nordstr\"om (RN) black hole in $F(R)$ gravity. It is remarkable that the effective electric charge can be generated for some solutions of $F(R)$ gravity without electromagnetic field. The anti-evaporation effect occurs but it emerges only in the strong coupling limit of the effective gravitational coupling. The instabilities of RN black hole are also investigated when the electromagnetic sector is added to the action of $F(R)$ gravity. We show the anti-evaporation occurs in the Maxwell-$F(R)$ gravity with the arbitrary gravitational coupling constant although it does not occur in the Maxwell-Einstein gravity. Furthermore, general spherically-symmetric solution of $F(R)$ gravity in the Einstein frame is obtained.