Black hole evaporation in Ho\u0159ava\u2013Lifshitz gravity

Hao Xu,Yen Chin Ong

doi:10.1140/epjc/s10052-020-8249-3

Abstract

Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter 0leqslant epsilon ^2leqslant 1. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with d=4,5 behave differently from dgeqslant 6. For the case of epsilon =0, in d=4,5, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As dgeqslant 6, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of ell ^{d-1}, similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to epsilon ^2=1), though for the latter this holds for all dgeqslant 4. The case of 0<epsilon ^2<1 is also qualitatively similar with epsilon =0.

Highlights

On the other hand, features of the evaporation process of black holes with nontrivial asymptotic behavior can be very different from their counterparts in the case of asymptotically flat spacetime
As d 6, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of d−1, similar to the case of Schwarzschild-AdS in Einstein gravity, though for the latter this holds for all d 4
On the other hand, is presented as an accidental symmetry at large distance, and the classical Einstein gravity is restored in the IR limit

Summary

Introduction

Features of the evaporation process of black holes with nontrivial asymptotic behavior can be very different from their counterparts in the case of asymptotically flat spacetime. Power-counting analysis shows that in order to have a renormalizable theory, the dimension of gravitational coupling constant should be larger than or equal to zero, otherwise the perturbative effective quantum field theory will break down at high energy, which is exactly what happens in Einstein gravity. Even in the limit λ = 1, in which the asymptotically AdS solutions can be obtained in the large distance approximation, these black holes have very different behaviors from their counterparts in Einstein gravity. In the present work we investigate the spherically symmetric neutral AdS black hole evaporation process in HL gravity, focusing on the λ = 1 and z = 3 with various spacetime dimensions d and detailed balance violation. We adapt the natural unit system, setting the speed of light in vacuum c, the gravitational constant G N , the Planck constant h and the Boltzmann constant k equal to one

Thermodynamics of Horava–Lifshitz Gravity

Summary