# Thermal activation of thin-shells in anti-de Sitter black hole spacetime

## TL;DR

This paper studies the thermal activation process of thin-shells around anti-de Sitter black holes, revealing conditions for bubble nucleation and black hole evaporation within a specific parameter space.

## Contribution

It provides a detailed analysis of bubble nucleation conditions and the role of conical deficits in Euclidean manifolds for AdS black holes.

## Key findings

- Finite range of black hole masses allows bubble nucleation.
- Complete black hole evaporation can occur within this process.
- Presence of conical deficits is essential for solutions with fixed external temperature.

## Abstract

We investigate thermal activation of thin-shells around anti-de Sitter black holes. Under the thin-shell approximation, we extensively study the parameter region that allows a bubble nucleation bounded by a thin-shell out of a thermal bath. We show that in general if one fixes the temperature outside the shell, one needs to consider the presence of a conical deficit inside the shell in the Euclidean manifold, due to the lack of solutions with a smooth manifold. We show that for a given set of theoretical parameters, i.e., vacuum and shell energy density, there is a finite range of black hole masses that allow this transition. Most interestingly, one of them describes the complete evaporation of the initial black hole.