https://doi.org/10.1140/epjc/s10052-021-09438-5
Regular Article - Theoretical Physics
Prospecting black hole thermodynamics with fractional quantum mechanics
1
Departamento de Física, Universidade Federal de Pernambuco, 52171-900, Recife, PE, Brazil
2
Departmento de Física, Universidade da Beira Interior, 6200, Covilhã, Portugal
3
Centro de Matemática e Aplicações (CMA-UBI), Covilhã, Portugal
Received:
11
March
2021
Accepted:
9
July
2021
Published online:
20
July
2021
This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) 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, 
. In particular, the standard results are recovered in the specific limit 
. Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.
© The Author(s) 2021
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