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

Abstract

In this letter we introduce the noncommutative geometry into the standard Einstein-Hilbert-Maxwell action via the ${\partial }_t\wedge {\partial }_{\ddot{I}}†$ 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 $T_{\hat{I}¼\hat{I}½}$ obtains correction terms with three Faraday tensors $F_{\hat{I}¼\hat{I}½}$. A solution with nonzero $a^1$ terms turns out to be the Kerr-Newman black hole modified with nonzero $g_{t\hat{I}¸},g_{r\ddot{I}†},g_{tr}$ and $g_{\ddot{I}†\hat{I}¸}$ components proportional to $a$, while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero $A_{\hat{I}}¸$ term proportional to $a$.

Final version of the paper, after positive review in Phys.Lett.B