Non-commutative black holes in $D$ dimensions

TL;DR

This paper explores a classical gravity theory in non-commutative geometry, identifying a family of D-dimensional black hole solutions with smooth horizons and analyzing their properties, including non-commutative effects as black hole hair.

Contribution

It introduces the most general four-parameter family of static spherically symmetric solutions in non-commutative gravity for D dimensions and studies their horizon and singularity structure.

Findings

Most solutions are asymptotically flat black holes with smooth horizons.

Non-commutative components of the metric act as black hole hair.

The solutions generalize known black hole models in non-commutative geometry.

Abstract

Recently introduced classical theory of gravity in non-commutative geometry is studied. The most general (four parametric) family of $D$ dibensional static spherically symmetric spacetimes is identified and its properties are studied in detail. For wide class of the choices of parameters, the corresponding spacetimes have the structure of asymptotically flat black holes with a smooth event horizon hiding the curvature singularity. A specific attention is devoted to the behavior of components of the metric in non-commutative direction, which are interpreted as the black hole hair.