Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics
arXiv:1812.10074 · doi:10.1103/PhysRevD.99.044028
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.
32 pages, 6 figures
References in corpus (24)
- The Confrontation between General Relativity and Experiment
- Healthy theories beyond Horndeski
- Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
- Exploring gravitational theories beyond Horndeski
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Higher-dimensional black holes with a conformally invariant Maxwell source
- Black holes with non-minimal derivative coupling
- Higher-dimensional charged black holes solutions with a nonlinear electrodynamics source
- Quintessence and phantom cosmology with non-minimal derivative coupling
- Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario
- Lovelock black holes with a nonlinear Maxwell field
- Vainshtein mechanism after GW170817
- UV-Protected Inflation
- Black Holes in Bi-scalar Extensions of Horndeski Theories
- Thermodynamics of higher dimensional topological dilaton black holes with power-law Maxwell field
- Thermodynamical First Laws of Black Holes in Quadratically-Extended Gravities
- Realistic cosmological scenario with non-minimal kinetic coupling
- Thermodynamics of a BTZ black hole solution with an Horndeski source
- Thermodynamics of Lifshitz Black Holes
- Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations
- SU(2)-Colored (A)dS Black Holes in Conformal Gravity
- Reheating predictions in Gravity Theories with Derivative Coupling
- Thermodynamics of Horndeski black holes with non-minimal derivative coupling
- Curvaton with Nonminimal Derivative Coupling to Gravity II: Full Perturbation Analysis