Statistical modeling of the fluid dual to Boulware-Deser Black hole

TL;DR

This paper models the horizon fluid of Boulware-Deser black holes in Einstein-Gauss-Bonnet gravity, revealing phase coexistence, excitations, and deriving the entropy consistent with Wald's formula.

Contribution

It introduces a statistical and thermodynamic model of the horizon fluid, capturing phase coexistence and excitations due to Gauss-Bonnet corrections, and clarifies the entropy expression.

Findings

Identification of two fluid phases: BEC and non-condensed.

Modeling of excitations with a generalized dispersion relation.

Derivation of horizon entropy matching Wald entropy.

Abstract

In this work we study the statistical and thermodynamic properties of the horizon fluid corresponding to the Boulware-Deser (BD) black hole of Einstein-Gauss-Bonnet (EGB) gravity. Using mean field theory, we show explicitly that the BD fluid exhibits the coexistence of two phases, a BEC and a non-condensed phase corresponding to the Einstein term and the Gauss-Bonnet term in the gravity action, respectively. In the fluid description, the high-energy corrections associated to Gauss-Bonnet gravity are modeled as excitations of the fluid medium. We provide statistical modeling of the excited part of the fluid and explicitly show that it is characterized by a generalized dispersion relation which in $D=6$ dimensions corresponds to a non-relativistic fluid. We also shed light on the ambiguity found in the literature regarding the expression of the entropy of the horizon fluid. We provide a general prescription to obtain the entropy and show that it is indeed given by Wald entropy.