Thermodynamics of Charged Brans-Dicke AdS Black Holes

Abstract

It is well-known that in four dimensions, black hole solution of the Brans-Dikce-Maxwell equations is just the Reissner-Nordstrom solution with a constant scalar field. However, in $n\ge 4$ dimensions, the solution is not yet the $(n+1)$-dimensional Reissner-Nordstrom solution and the scalar field is not a constant in general. In this paper, by applying a conformal transformation to the dilaton gravity theory, we derive a class of black hole solutions in $(n+1)$-dimensional $(n\ge 4)$ Brans-Dikce-Maxwell theory in the background of anti-de Sitter universe. We obtain the conserved and thermodynamic quantities through the use of the Euclidean action method. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble. We find that the solution is thermally stable for small $\alpha$, while for large $\alpha$ the system has an unstable phase, where $\alpha$ is a coupling constant between the scalar and matter field.

14 pages, one figure, to appear in Phys. Lett. B

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• Exact black hole solution for scale dependent gravitational couplings and the corresponding coupling flow
• Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames
• Lifshitz black holes in Brans-Dicke theory
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Topological dyonic dilaton black holes in AdS spaces
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Transport in a gravity dual with a varying gravitational coupling constant
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• Magnetic Branes in Brans-Dicke-Maxwell Theory