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

In this letter we introduce the noncommutative geometry into the standard Einstein-Hilbert-Maxwell action via the ${\mathrm{\partial }}_t\wedge {\mathrm{\partial }}_{\phi }$ 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 $g_{t\theta },g_{r\phi },g_{tr}$ and $g_{\phi \theta }$ 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 $a$.