Abstract
We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity. Since cosmological constant is taken into account it allowed us not only derive static black hole with spherical horizon but also to obtain topological solutions with non-spherical horizons. The obtained metrics are thoroughly analyzed, namely for different distances and types of topology of horizon. To investigate singularities of the metrics Kretschmann scalar is used and it is shown that the character of singularity depends on the type of topology of horizon and dimension of space. We also investigate black hole's thermodynamics, namely we obtain and examine black hole's temperature. To derive the first law of black hole's thermodynamics Wald's approach is applied. Nonetheless this approach is well established, there is ambiguity in definition of black hole's entropy which can be resolved just by virtue of some independent approach.
Highlights
General relativity is extremely successful theory which explains vast range of gravitational phenomena starting from the planetary motion and up to the evolution of the Universe [1,2]
Numerous observations in astrophysics go hand in hand with theoretically predicted values [3], but there are still some open issues that give a chance for new theories which can be treated as generalization of Einsteinian general relativity [4,5]
In this work we consider a particular case of Horndeski gravity, namely the theory with nonminimal derivative coupling and we take into account nonlinear electromagnetic field of Born-Infeld type which is minimally coupled to gravity
Summary
General relativity is extremely successful theory which explains vast range of gravitational phenomena starting from the planetary motion and up to the evolution of the Universe [1,2]. In this work we consider a particular case of Horndeski gravity, namely the theory with nonminimal derivative coupling and we take into account nonlinear electromagnetic field of Born-Infeld type which is minimally coupled to gravity. Within this framework we find static solutions of field equations which represent black holes. In the third section we investigate some aspects of thermodynamics of the black hole, namely the behavior of its temperature is studied and it is compared with the results derived for the linear Maxwell field [54,55], in the second part of this section we obtain the first law of black hole’s thermodynamics using Wald’s approach.
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