Abstract
We obtain topological black hole solutions in scalar-tensor gravity with nonminimal derivative coupling between scalar and tensor components of gravity and power-law Maxwell field minimally coupled to gravity. The obtained solutions can be treated as a generalization of previously derived charged solutions with standard Maxwell action \cite{Feng_PRD16}. We examine the behaviour of obtained metric functions for some asymptotic values of distance and coupling. To obtain information about singularities of the metrics we calculate Kretschmann scalar. We also examine the behaviour of gauge potential and show that it is necessary to impose some constraints on parameter of nonlinearity in order to obtain reasonable behaviour of the filed. The next part of our work is devoted to the examination of black hole's thermodynamics. Namely we obtain black hole's temperature and investigate it in general as well as in some particular cases. To introduce entropy we use well known Wald procedure which can be applied to quite general diffeomorphism-invariant theories. We also extend thermodynamic phase space by introducing thermodynamic pressure related to cosmological constant and as a result we derive generalized first law and Smarr relation. The extended thermodynamic variables also allow us to construct Gibbs free energy and its examination gives important information about thermodynamic stability and phase transitions. We also calculate heat capacity of the black holes which demonstrates variety of behaviour for different values of allowed parameters.
Highlights
General relativity is a renowned theory that gives explanations for numerous facts and is in agreement with lots of observations ranging from planetary scales to cosmological ones [1,2]
As it has been noted above charged topological black holes in Einstein-Horndeski gravity with standard Maxwell action term were considered and their thermodynamics was studied in the paper [59]
We examine topological black holes in the theory with nonminimal derivative coupling between tensor and scalar components and nonlinear Maxwell field with a Lagrangian of the power-law type
Summary
General relativity is a renowned theory that gives explanations for numerous facts and is in agreement with lots of observations ranging from planetary scales to cosmological ones [1,2]. As it has been noted above charged topological black holes in Einstein-Horndeski gravity with standard (linear) Maxwell action term were considered and their thermodynamics was studied in the paper [59]. We examine topological black holes in the theory with nonminimal derivative coupling between tensor and scalar components and nonlinear Maxwell field with a Lagrangian of the power-law type. We derive topological black hole solutions and investigate the behavior of metric functions for different distances and regimes of coupling, we examine Kretschmann scalar in order to make some conclusions about singular points of the obtained solution, we obtain gauge potential and derive some constraints on parameter of nonlinearity in order to have this potential reasonable.
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