# Hawking-R\'enyi thermodynamics of rotating black holes from locally Kiselev-type behavior

## TL;DR

This paper explores the thermodynamics of rotating black holes using the Hawking-Rényi model, demonstrating that a locally Kiselev-type anisotropic fluid can reconcile the Re9nyi entropy with surface gravity, with implications for charged and uncharged black holes.

## Contribution

It introduces a locally Kiselev-type behavior to solve the temperature equivalence problem in Hawking-Re9nyi thermodynamics for rotating black holes, including charge effects.

## Key findings

- Solution form is consistent for charged and uncharged black holes.
- A coupled anisotropic fluid near the horizon enables temperature matching.
- Rotation affects the effective mass through a shift depending on rotation and Re9nyi parameters.

## Abstract

The Hawking-R\'enyi model requires the R\'enyi 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 R\'enyi parameter, $\lambda$. 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.