Non-commutative geometry inspired higher-dimensional charged, black holes

TL;DR

This paper presents an exact higher-dimensional charged black hole solution inspired by non-commutative geometry, which is regular, interpolates between known geometries, and has well-studied thermodynamics and pair creation properties.

Contribution

It introduces a novel, exact, regular black hole solution in higher dimensions incorporating quantum gravitational effects via non-commutative geometry.

Findings

The black hole solution is regular and free of singularities.

Thermodynamics and Area Law are characterized for the new solution.

Pair creation and discharge times are analyzed with respect to extra dimensions.

Abstract

We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. De-localization of mass and charge is due to the presence of a "minimal length" in the spacetime fabric, coming from quantum gravitational effects, e.g. string induced non-commutative geometry. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner-Nordstrom geometry at large distance, and deSitter spacetime at short distance. Thermodynamical properties of the black hole are investigated and the form of the Area Law is determined. We show that back reaction effects are negligible even near the temperature maximum for any reasonable number of extra dimensions. We study pair creation and show that the upper bound on the discharge time increases with the number of extra dimensions.