A non commutative model for a mini black hole

TL;DR

This paper models a mini black hole using non-commutative geometry, replacing the singularity with a finite droplet of anisotropic fluid, and analyzes its properties within Einstein's equations.

Contribution

It introduces a novel non-commutative geometry-inspired model of a mini black hole with a finite droplet replacing the singularity.

Findings

The solution has Schwarzschild geometry outside the horizon.

The central singularity is replaced by a finite, self-gravitating droplet.

The interior pressure is positive and supports hydrostatic equilibrium.

Abstract

We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole which has the Schwarzschild geometry outside the event horizon, but whose standard central singularity is replaced by a self-gravitating droplet. The energy-momentum tensor of the droplet is of the anisotropic fluid obeying a nonlocal equation of state. The radius of the droplet is finite and the pressure, which gives rise to the hydrostatic equilibrium, is positive definite in the interior.