Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon

Abstract

We demonstrate that the implementation of the fractional and non-local Wheeler--DeWitt (WDW) equation within the context of Schwarzschild geometry leads to the emergence of a Schwarzschild--Tangherlini black hole (BH), which is uniquely characterized by an event horizon that exhibits fractal properties and is defined by a non-integer dimension that lies in the continuum between the values of 1 and 2. Our calculations further reveal that this intriguing fractional BH may potentially possess a temperature that is substantially lower than that of a conventional BH, thereby suggesting a significant deviation from the expected thermodynamic properties of standard BHs. These remarkable characteristics, which are intrinsically linked to the non-integer dimensionality of the event horizon, likely arise from applying the Riesz fractional derivative as a sophisticated non-local operator, thus introducing fascinating dynamics into the theoretical framework of BH physics.

10 pages, 3 figures

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Cited by in corpus (5)

• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Finite Hilbert space and maximum mass of Schwarzschild black holes from a Generalized Uncertainty Principle
• Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action
• Constraining fractionality using some observational tests
• Hawking area law in quantum gravity