The fate of Schwarzschild-de Sitter Black Holes in $f(R)$ gravity

TL;DR

This paper investigates how $f(R)$ gravity influences the stability and evolution of Schwarzschild-de Sitter black holes, revealing that antievaporation prevents Hawking radiation emission in certain black hole configurations.

Contribution

It demonstrates the impact of $f(R)$ gravity on black hole horizon dynamics and the suppression of thermal radiation in antievaporating Nariai black holes.

Findings

Antievaporation leads to horizon growth in $f(R)$ gravity.

Thermal radiation emission is suppressed before the Hawking emission time.

Implications for black hole evolution and cosmology are discussed.

Abstract

The semiclassical effects of antievaporating black holes can be discussed in the framework of $f(R)$ gravity. In particular, the Bousso-Hawking-Nojiri-Odinstov antievaporation instability of degenerate Schwarzschild-de Sitter black holes (the so called Nariai space-time) leads to a dynamical increasing of black hole horizon in $f(R)$ gravity. This phenomenon causes the following transition: emitting marginally trapped surfaces become space-like surfaces before the effective Bekenstein-Hawking emission time. As a consequence, Bousso-Hawking thermal radiation cannot be emitted in an antievaporating Nariai black hole. Possible implications in cosmology and black hole physics are also discussed.