AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity

TL;DR

This paper explores how Horndeski gravity modifies the AdS/BCFT correspondence and BTZ black hole thermodynamics, revealing effects on boundary entropy, phase transitions, and conformal symmetry restoration at high temperatures.

Contribution

It introduces a novel analysis of 3D BTZ black holes within Horndeski gravity in the AdS/BCFT framework, extending Takayanagi's boundary entropy concept.

Findings

Horndeski gravity affects boundary entropy calculations.

High temperatures restore conformal symmetry.

Hawking-Page phase transition exhibits stable and unstable phases.

Abstract

In this work, we study gravity duals of conformal field theories with boundaries known as AdS/BCFT correspondence, put forward by Takayanagi [1], within a scalar-tensor theory, as proposed by Horndeski in 4D [2]. We consider the case of 3D gravity dual to 2D BCFT, take a Gibbons-Hawking surface term modified by Horndeski's theory and find the corresponding 3D (BTZ) black hole solutions. We analyze the effects of Horndeski's gravity on the profile of the extra boundary for the black hole by using an approximate analytic solution. Performing a holographic renormalization, we have calculated the free energy and obtained the total entropy and the corresponding area, as well as the boundary entropy for the black hole. In particular, the boundary entropy found here, can be seen as an extension of the one proposed by Takayanagi. From the free energy, we have done a systematic study of the 3D black hole thermodynamics and present, among our results, an indication of restoration of conformal symmetry for high temperatures. Finally, we present a study on the influence of the Horndeski's gravity on the Hawking-Page phase transition where we can see the stable and unstable phases throughout the plane of free energy {\sl versus} temperature.