# Black hole evaporation in Lovelock gravity with diverse dimensions

## TL;DR

This paper studies black hole evaporation in Lovelock gravity across various dimensions, revealing different behaviors depending on the relation between dimension and Lovelock order, including bounded lifetime and infinite evaporation time.

## Contribution

It provides a detailed analysis of black hole evaporation in Lovelock gravity with diverse dimensions, extending known results and exploring the effects of higher-order curvature terms.

## Key findings

- Black hole lifetime bounded by a dimension-dependent scale in certain cases.
- Black holes in odd dimensions take infinite time to evaporate, consistent with the third law of thermodynamics.
- In the flat limit, the lifetime scales with initial mass raised to a specific power.

## Abstract

We investigate the black hole evaporation process in Lovelock gravity with diverse dimensions. By selecting the appropriate coefficients, the space-time solutions can possess a unique AdS vacuum with a fixed cosmological constant $\Lambda=-\frac{(d-1)(d-2)}{2\ell^{2}}$. The black hole solutions can be divided into two cases: $d>2k+1$ and $d=2k+1$. In the case of $d>2k+1$, the black hole is in an analogy with the Schwarzschild AdS black hole, and the life time is bounded by a time of the order of $\ell^{d-2k+1}$, which reduces Page's result on the Einstein gravity in $k=1$. In the case of $d=2k+1$, the black hole resembles the three dimensional black hole. The black hole vacuum corresponds to $T=0$, so the black hole will take infinite time to evaporate away for any initial states, which obeys the third law of thermodynamics. In the asymptotically flat limit $\ell\rightarrow \infty$, the system reduces to the pure Lovelock gravity that only possesses the highest $k$-th order term. For a initial mass $M_0$, the life time of the black hole is in the order of $M_0^{\frac{d-2k+1}{d-2k-1}}$.