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

Abstract The thermodynamics of black holes (BHs) has had a profound impact on theoretical physics, providing insight into the nature of gravity, the quantum structure of spacetime and the fundamental laws governing the Universe. In this study, we investigate thermal geometries and Hawking evaporation of the recently proposed topological dyonic dilaton BH in anti-de Sitter (AdS) space. We consider Rényi entropy and obtain the relations for pressure, heat capacity and Gibbs free energy and observe that the Rényi parameter and dilaton field play a vital role in the phase transition and stability of the BH. Moreover, we use Weinhold, Ruppeiner and Hendi Panahiyah Eslam Momennia models to evaluate the scalar curvature of the BH and find out that the divergence points of the scalar curvature coincides with the zero of specific heat. Finally, using Stefan–Boltzmann law, we determine that the BH without a dilaton field evaporates far more quickly compared to the dilaton BH in AdS space.

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