Deviation from the First Law of Thermodynamics for Particle-like Quantum Kerr-de Sitter Black Holes

TL;DR

This paper extends a quantum black hole quantization scheme to extremal Kerr-de Sitter black holes and finds a measurable deviation from the First Law of thermodynamics that depends on the cosmological constant.

Contribution

It introduces a quantum scheme for extremal Kerr-de Sitter black holes and quantifies deviations from thermodynamic laws in these systems.

Findings

Quantized parameters match existing results in proper limits.

Deviations from the First Law scale with the cosmological constant.

Numerical analysis shows a root mean square deviation of order Λ^{0.45 ± 0.01}.

Abstract

The goal of this paper is to extend the particle-like quantization scheme presented in Pacheco and Silk (2020), to extremal Kerr-de Sitter black holes in four spacetime dimensions, thereby obtaining various quantized parameters, like the black hole mass and angular momentum, consistent with existing results, in the proper limits. Moreover, we show numerically, that for such extremal quantum black holes, there is a root mean square deviation from the First Law of black hole thermodynamics, of the order $\mathcal{O}(\Lambda^{0.45 \pm 0.01})$, where $\Lambda$ denotes the Cosmological Constant.