On the scalar-vector-tensor gravity: Black hole, thermodynamics and geometrothermodynamics

Recently, a new class of modified gravity theories formulated via an additional scalar and vector field on top of the standard tensor field has been proposed. The direct implications of these theories are expected to be relevant for cosmology and astrophysics. In the present work, we revisit the modified framework of the scalar-vector-tensor theories of gravity. Surprisingly, we discover novel metric function for the black hole solutions. We also investigate the semi-classical thermodynamics of the black holes and study the thermodynamic properties of the obtained solutions. Moreover, we quantify the entropy and the temperature of the new black hole and also calculate the heat capacity. Finally, we also apply the formalism of the geometrothermodynamics to examine thermodynamic properties of the new black hole. This formalism yields results consistent with those obtained from the usual thermodynamic implementation.