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arXiv · 0904.1777

Thermodynamics of Charged Brans-Dicke AdS Black Holes

A. Sheykhi·M. M. Yazdanpanah
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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 $n\geq4$ 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 $(n\geq 4)$ 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 $α$, while for large $α$ the system has an unstable phase, where $α$ is a coupling constant between the scalar and matter field.

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A. Sheykhi, M. M. Yazdanpanah. 2009-08-01. Thermodynamics of Charged Brans-Dicke AdS Black Holes. https://doi.org/10.1016/j.physletb.2009.07.056

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