Consequences of Rényi entropy on the thermal geometries and Hawking evaporation of topological dyonic dilaton black hole

Abstract

The thermodynamics of black holes has had a profound impact on theoretical
physics, providing insights into the nature of gravity, the quantum structure of
spacetime, and the fundamental laws governing the universe. In this work, we
study thermal geometries and Hawking evaporation of recently proposed topological
dyonic dilaton black hole in AdS space. We consider Renyi entropy and obtain
the relations for pressure, heat capacity and Gibbs free energy and observe that
the Renyi parameter and dilaton ¯eld has vital role on the phase transition and
stability of the BH. Moreover, we use Weinhold, Ruppeiner and Hendi Panahiyah
Eslam Momennia models to evaluate scalar curvature of the BH and ¯nd out that
the divergence points of the scalar curvature coincides with the zero of speci¯c heat.
Finally using Stefan-Boltzmann law, we analyze that black hole without dilaton
¯eld evaporate far more quickly as compare to dilaton black hole in AdS space.