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

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 versus temperature.

Entanglement Entropy in Horndeski Gravity

“…This fact, agree with Ryu-Takayanagi formula as shown in (52). This first law of entanglement thermodynamics in Horndeski gravity in fact agree with the result of [19,[25][26][27].…”

“…In this section we address the issue of finding black hole solutions in Horndeski gravity [17][18][19][30][31][32][33][34]. Black holes in Horndeski's theory have been previously studied in [17-19, 31, 32, 34].…”

“…The solution (13) corresponds to black hole solution for asymptotically AdS 4 spacetime [34]. Beyond, through Λ = −3/R 2 and considering the analyses of [17][18][19] in our prescription, we can write the black hole solution…”

“…The main motivation to investigate the play role of Horndeski gravity in the entanglement entropy scenario is due the recent investigations of the AdS/CFT correspondence in this gravity [17][18][19][20][21][22][23][24][25][26][27][28]. Besides, beyond to the classes of boundary field theories that were studied by Ryu and Takayanagi [7,8] other classes were proposed using this conjecture, such as AdS black holes with dual charge in the bulk [11][12][13].…”

“…For this boundary field theory at finite temperature, we address the issues to related to entanglement thermodynamics within Horndeski gravity in our setup, for more discussion about this see [10,[14][15][16]. For the avaible the excited states we compute the stress-energy tensor of boundary field theory in Horndeski gravity following the prescription of [19,29].…”