# Evaporation and anti-evaporation instability of a Schwarzschild-de Sitter braneworld: the case of five-dimensional F(R) gravity

## TL;DR

This paper investigates the stability of a four-dimensional brane within a five-dimensional Schwarzschild-de Sitter black hole in F(R) gravity, revealing conditions for brane existence and identifying classical evaporation instabilities in the bulk.

## Contribution

It demonstrates the non-existence of the brane in Nariai bulk unless brane tension is zero and uncovers classical anti-evaporation instabilities in the five-dimensional F(R) gravity setting.

## Key findings

- Brane cannot exist in Nariai bulk unless tension vanishes.
- The five-dimensional Nariai bulk exhibits classical anti-evaporation instabilities.
- Bulk instabilities influence the brane's dynamics when tension is zero.

## Abstract

We study the problem of a four-dimensional brane lying in the five-dimensional degenerate Schwarzschild-de Sitter (Nariai) black hole, in five-dimensional $F(R)$-gravity. We show that there cannot exist the brane in the Nariai bulk space except the case that the brane tension vanishes. We demonstrate that the five-dimensional Nariai bulk is unstable in a large region of the parameter space. In particular, the Nariai bulk can have classical (anti-)evaporation instabilities. The bulk instability back-reacts on the four-dimensional brane, in case that the brane tension vanishes, and the unstable modes propagate in their world-volume.