RPST-Inspired Formalism for Black Holes in Flat Spacetime

TL;DR

This paper introduces a new thermodynamic formalism for flat black holes inspired by RPST, replacing the cosmological constant with a deformation parameter, and demonstrates its application to RN and Kerr black holes.

Contribution

It extends the RPST framework to non-AdS black holes by introducing a deformation parameter and response potential, enabling thermodynamic analysis without a cosmological constant.

Findings

Formalism successfully applied to RN flat black hole

Formalism successfully applied to Kerr black hole

Provides new insights into flat black hole thermodynamics

Abstract

In this work, we propose a novel formalism for the thermodynamics of flat black holes, inspired by the Restricted Phase Space Thermodynamics (RPST) framework. Our construction is motivated by the observed similarities in the thermodynamic behavior of flat black holes within the R\'enyi entropy framework and that of AdS black holes described by the Bekenstein entropy regime. The RPST framework is, by construction, exclusive to AdS black holes because it depends on the cosmological constant $\Lambda$, which is linked to the central charge $C$ of the dual conformal field theory (CFT). However, for non-AdS black holes, where $\Lambda$ is absent, we introduce a deformation parameter $\lambda$ to replace the central charge $C$. This RPST-inspired formalism incorporates $\lambda$ and its conjugate variable, the response potential $\zeta$, as a new pair of thermodynamic variables, analogous to the central charge $C$ and chemical potential $\mu$ in the AdS case. To illustrate the applicability of this formalism, we analyze two examples: the Reissner-Nordstr\"om (RN) flat black hole and the Kerr black hole.