Black hole solutions in gravity with nonminimal derivative coupling and nonlinear material fields

Abstract

Scalar–tensor theory of gravity with nonlinear electromagnetic field, minimally coupled to gravity is considered and static black hole solutions are obtained. Namely, power-law and Born–Infeld nonlinear Lagrangians for the electromagnetic field are examined. Since the cosmological constant is taken into account, it allowed us to investigate the so-called topological black holes. Black hole thermodynamics is studied, in particular temperature of the black holes is calculated and examined and the first law of thermodynamics is obtained with help of Wald’s approach.