Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics

TL;DR

This paper explores how fractional quantum mechanics modifies black hole thermodynamics, revealing new relationships between black hole properties and fractional parameters, and connecting generalized entropy concepts to fractional frameworks.

Contribution

It introduces a fractional quantum mechanics approach to black hole thermodynamics, deriving modified observables and linking generalized entropy-area relations to fractional parameters.

Findings

Standard results recovered at fractional parameter $ ext{α}=2$

Black hole mass, temperature, and entropy are altered by fractional derivatives

Generalized entropy relations can be interpreted through fractional quantum mechanics

Abstract

This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a {\it space-fractional} derivative \cite{Rie} as our main tool. Moreover, we restrict our analysis to the case of a Schwarzschild configuration. From a subsequently modified Wheeler-DeWitt equation, we retrieve the corresponding expressions for specific observables. Namely, the black hole mass spectrum, $M$, its temperature $T$, and entropy, $S$. We find that these bear consequential alterations conveyed through a fractional parameter, $\alpha$. In particular, the standard results are recovered in the specific limit $\alpha=2$. Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto \cite{Tsallis} and Barrow \cite{Barrow} acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.