Corrections to Kerr-Newman black hole from noncommutative Einstein-Maxwell equation - Filip Požar (Physics Letters B)
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 Tμν obtains correction terms with three Faraday tensors Fμν. A solution with nonzero a1 terms turns out to be the Kerr-Newman black hole modified with nonzero gtθ,grφ,gtr and gφθ components proportional to a, while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero Aθ term proportional to a.