Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon

TL;DR

This paper introduces a fractional Schwarzschild-Tangherlini black hole with a fractal event horizon, derived from a non-local Wheeler--DeWitt equation, revealing novel thermodynamic and geometric properties due to non-integer dimensionality.

Contribution

It presents a new model of black holes with fractal horizons using fractional calculus, expanding the understanding of black hole geometry and thermodynamics.

Findings

Event horizon exhibits fractal properties with non-integer dimension.

Black hole temperature may be significantly lower than classical predictions.

Fractal horizon linked to non-local fractional derivatives in quantum gravity.

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.