# Temperature of McVittie Black Holes in Cavities

## TL;DR

This paper investigates the temperature of dynamical McVittie black holes within isothermal cavities, deriving a simpler method to calculate their temperature that aligns with existing results for de Sitter black holes.

## Contribution

It introduces a new, easier approach to determine the temperature of McVittie black holes in cavities, overcoming challenges of traditional methods for dynamical black holes.

## Key findings

- Derived cavity temperature from McVittie black hole temperature and Tolman relation.
- Found that cavity temperature matches de Sitter black hole results when setting H^2 to Λ/3.
- Proposed a simpler method for temperature calculation of dynamical black holes.

## Abstract

In this paper, we study the temperature of the McVittie black holes in cavities. The cavities are isothermal boxes that can make the McVittie black holes thermodynamically stable. The McVittie black holes are dynamical black holes, so the traditional action method can hardly be used to calculate the cavity temperature. We find that the cavity temperature $T_c$ can be derived from the McVittie black hole temperature $T_+$ and the Tolman relation. By setting $H^2$ to be $\Lambda/3$, we also get the cavity temperature of de Sitter black holes, which are interestingly the same with the results from the action method, but our method is much more easier.