Emergent Abelian Gauge Fields from Noncommutative Gravity

TL;DR

This paper constructs exact solutions in noncommutative gravity that naturally include Abelian gauge fields, offering a mechanism for cosmological electromagnetic field generation and black hole multipole structures.

Contribution

It demonstrates that noncommutative gravity solutions inherently produce Abelian gauge fields at first order, linking noncommutative geometry to observable electromagnetic phenomena.

Findings

Generation of cosmological electromagnetic fields in expanding space-time.

Multipole-like electromagnetic fields around black holes.

First order corrections to black hole horizons.

Abstract

We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.