Black Hole with Non-Commutative Hair

TL;DR

This paper presents a new type of asymptotically flat black hole solution with non-commutative vector hair, challenging the traditional no-hair theorem by solving Einstein gravity coupled with a nonlinear vector sigma-model.

Contribution

It introduces a novel black hole solution with non-commutative vector hair within a specific nonlinear sigma-model coupled to gravity, providing a counterexample to the no-hair theorem.

Findings

Black hole with non-commutative vector hair exists

Solution is asymptotically flat

Counterexample to no-hair theorem

Abstract

The specific nonlinear vector $\sigma$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative'' vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair'' theorem.