Non-extensive and quasi-homogeneous black hole thermodynamics

Abstract: We study the thermodynamic properties of black holes, taking into account the non-extensivity of their entropy at the thermodynamic and statistical level. To this end, we interpret the R\'enyi entropy as determining the fundamental thermodynamic equation, which is represented by a quasi-homogeneous function. As a consequence, the R\'enyi parameter turns out to be an independent thermodynamic variable that must be treated in the framework of extended thermodynamics. As a particular example, we use the formalism of geometrothermodynamics to show that the Schwarzschild black hole can become stable for certain values of the R\'enyi parameter.