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 {\sl versus} temperature.

arXiv commentV2: 32 pages, 7 figures. Text improved. Typos corrected. New references added. Results unchanged. This version matches the published one in PRD

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• Magnetized AdS/BCFT Correspondence in Horndeski Gravity
• Transport properties in the Horndeski holographic two-currents model
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• Three-dimensional energy-dependent $C$-metric: black hole solutions
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• Black branes in asymptotically Lifshitz spacetimes in $\kappa$-deformed Horndeski gravity
• Holographic Boundary Conformal Field Theory within Horndeski Gravity
• Phantom BTZ black holes
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• Topological 4D gravity and gravitational defects
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• Vector mesons from a holographic QCD model in $f(R)$-dilaton gravity
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