Thermodynamics of Charged Brans-Dicke AdS Black Holes

Understand

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.