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 ∂ t ∧ ∂ φ 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 μ ν obtains correction terms with three Faraday tensors F μ ν . A solution with nonzero a 1 terms turns out to be the Kerr-Newman black hole modified with nonzero g t θ , g r φ , g t r and g φ θ components proportional to a , while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero A θ term proportional to a .