Hawking–Rényi thermodynamics of rotating black holes from locally Kiselev-type behavior

Abstract The Hawking–Rényi model requires the Rényi entropy thermodynamic temperature of a black hole to be identical with the surface gravity defined-, Hawking temperature. We investigate this approach for stationary black hole space-times, and show that a locally Kiselev-type behavior around the horizon with a coupled anisotropic fluid is sufficient to provide a solution to the problem. In addition, due to the rotating motion, an extra shift has also to be present in the effective mass of the black hole, which is determined by the rotation parameter, a , and the Rényi parameter, $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> . We consider space-times with and without electric charge, and show that the functional form of the solution is the same for both cases. A full thermodynamic analysis of the model falls beyond the scope of this Letter, the main achievements are the derivation and interpretation of the solution.