Corrections to Kerr-Newman black hole from Noncommutative Einstein-Maxwell equation

TL;DR

This paper introduces noncommutative geometry into the Einstein-Maxwell theory to derive corrections to the Kerr-Newman black hole, resulting in modified metric and electromagnetic potential components.

Contribution

It presents a perturbative solution incorporating noncommutative effects into the Kerr-Newman black hole, a novel approach in noncommutative gravity research.

Findings

Modified Kerr-Newman metric with nonzero off-diagonal components

Electromagnetic potential gains a nonzero θ component due to noncommutativity

Noncommutative corrections appear at first order in the parameter a

Abstract

In this letter we introduce the noncommutative geometry into the standard Einstein-Hilbert-Maxwell action via the $\partial_t\wedge\partial_\varphi$ Drinfeld twist and solve the equation of motion pertubatively in the expansion of the noncommutative parameter $a$. The equation of motion, the NC Einstein-Maxwell equation, turns out to be effectively a problem in nonlinear electrodynamics where the energy-momentum tensor $T_{\mu\nu}$ obtains correction terms with three Faraday tensors $F_{\mu\nu}$. A solution with nonzero $a^1$ terms turns out to be the Kerr-Newman black hole modified with nonzero $g_{t\theta}, g_{r\varphi}, g_{tr}$ and $g_{\varphi\theta}$ components proportional to $a$, while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero $A_{\theta}$ term proportional to $a$.