# Regular black holes with $\Lambda>0$ and its evolution in Lovelock gravity

## TL;DR

This paper investigates the thermodynamic evolution of regular black holes with a positive cosmological constant in Lovelock gravity, revealing phase transitions and possible end states differing from standard de Sitter evolution.

## Contribution

It demonstrates that regular black holes in Lovelock gravity evolve towards thermal equilibrium or extremality, introducing a local first law of thermodynamics at each horizon.

## Key findings

- Black holes evolve into thermal equilibrium or extremal states.
- A phase transition in heat capacity influences black hole evolution.
- A local first law of thermodynamics is derived at each horizon.

## Abstract

In this work it is shown that the thermodynamics of regular black holes with a cosmological horizon, which are solutions of Lovelock gravity, determines that they must evolve either into a state where the black hole and cosmological horizons have reached thermal equilibrium or into an extreme black hole geometry where the black hole and cosmological horizons have merged. This differs from the behavior of Schwarzschild de Sitter geometry which evolves into a de Sitter space, the ground state of the space of solutions. This occurs due to a phase transition of the heat capacity of the black hole horizon. To perform that analysis it is shown that at each horizon a local first law of thermodynamics can be obtained from the gravitational equations.