High dimensional AdS-like black hole and Phase transition in Einstein-bumblebee gravity

TL;DR

This paper derives an exact high-dimensional AdS black hole solution in Einstein-bumblebee gravity, explores its thermodynamics, and identifies phase transitions influenced by Lorentz symmetry breaking.

Contribution

It presents the first exact high-dimensional AdS black hole solution in Einstein-bumblebee gravity with Lorentz symmetry breaking effects.

Findings

Existence of small-large black hole phase transition.

Presence of Hawking-Page phase transition.

Lorentz symmetry breaking lowers the black hole mass at heat capacity divergence.

Abstract

In this paper we obtain an exact high dimensional anti-de Sitter (AdS) black hole solution in Einstein-bumblebee gravity theory. This AdS-like black hole can only exist with a linear functional potential of the bumblebee field. We find that the Smarr formula and the first law of black hole thermodynamics can still be constructed in this Lorentz symmetry breaking black hole spacetime as long as its temperature, entropy and volume are slightly modified. We find also that there exist two kinds of phase transition: small-large black hole phase transition and Hawking-Page phase transition, like those of Schwarzschild AdS black hole. After Lorentz symmetry breaking, the black hole mass at divergent point of heat capacity becomes small, and the Gibbs free energy of the meta-stable large black hole is also smaller, showing that the large stable black hole can be more easily formed.