Black hole remnant in asymptotic anti-de Sitter space

Wen-Yu Wen,Shang-Yu Wu

doi:10.1140/epjc/s10052-015-3841-7

Abstract

It is known that a solution of remnant were suggested for black hole ground state after surface gravity is corrected by loop quantum effect. On the other hand, a Schwarzschild black hole in asymptotic Anti-de Sitter space would tunnel into the thermal soliton solution known as the Hawking-Page phase transition. In this letter, we investigate the low temperature phase of three-dimensional BTZ black hole and four-dimensional AdS Schwarzschild black hole. We find that the thermal soliton is energetically favored than the remnant solution at low temperature in three dimensions, while Planck-size remnant is still possible in four dimensions. Though the BTZ remnant seems energetically disfavored, we argue that it is still possible to be found in the overcooled phase if strings were present and its implication is discussed.

Highlights

It is well known that a Schwarzschild black hole in asymptotic anti-de Sitter space would tunnel into the thermal AdS solution known as the Hawking–Page phase transition [5,6]
We investigated the low temperature phase of the three-dimensional BTZ black hole and the four-dimensional AdS Schwarzschild black hole
We found that the thermal AdS is energetically favored rather than the remnant solution at low temperature in three dimensions, while a Planck-size remnant is still possible in four dimensions for a negative one-loop coefficient

Summary

Introduction

It is well known that a Schwarzschild black hole in asymptotic anti-de Sitter space would tunnel into the thermal AdS solution known as the Hawking–Page phase transition [5,6]. One needs to assume that both the first law of thermodynamics and the logarithmic correction to the black hole entropy are valid within the energy range in our discussion The extrapolation of both relations to the limit of the Planck size may be too naive, especially as regards our ignorance of a complete theory of quantum gravity. Our strategy is to compare the free energy of the remnant and that of the thermal AdS around the Hawking– Page temperature TH P = 1/2πl This corresponds to the energy scale O(l−1), which is still far from the Planck or string scale; it should be reasonable to assume that the laws of thermodynamics are valid and the black hole size around O(l) can be treated as a classical and static background. 3, we compute the up to two loops corrected entropy and free energy for the BTZ black hole and discuss its phase transition to thermal AdS. We discuss possible scenarios around the phase transition if a stringy excitation is considered

BTZ black hole and Hawking–Page phase transition

Quantum correction to surface gravity and the emergence of the remnant

Schwarzschild–AdS4 black hole

Implication of AdS remnant

Stringy point of view

Summary