Regular Black Holes and Noncommutative Geometry Inspired Fuzzy Sources

TL;DR

This paper explores regular black holes with fuzzy, noncommutative geometry-inspired sources in three and four dimensions, analyzing horizon formation and the role of voids near the center, with specific models like fuzzy discs.

Contribution

It introduces new models of regular black holes with Gaussian-based fuzzy sources and examines how spacetime dimensions influence horizon structure and the significance of central voids.

Findings

Number of horizons depends on spacetime dimension.

Existence of a void near the center is crucial, more than noncommutativity.

Horizon formation conditions are derived for specific fuzzy source models.

Abstract

We investigated regular black holes with fuzzy sources in three and four dimensions. The density distributions of such fuzzy sources are inspired by noncommutative geometry and given by Gaussian or generalized Gaussian functions. We utilized mass functions to give a physical interpretation of the horizon formation condition for the black holes. In particular, we investigated three-dimensional BTZ-like black holes and four-dimensional Schwarzschild-like black holes in detail, and found that the number of horizons is related to the spacetime dimensions, and the existence of a void in the vicinity of the center of the spacetime is significant, rather than noncommutativity. As an application, we considered a three-dimensional black hole with the fuzzy disc which is a disc-shaped region known in the context of noncommutative geometry as a source. We also analyzed a four-dimensional black hole with a source whose density distribution is an extension of the fuzzy disc, and investigated the horizon formation condition for it.