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arXiv · 2502.03337

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

Filip Požar
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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 $a$.

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Filip Požar. 2025-02-05. Corrections to Kerr-Newman black hole from Noncommutative Einstein-Maxwell equation. https://doi.org/10.1016/j.physletb.2025.139751

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