Caged black hole with Maxwell charge
  We construct the perturbative solution of the charged black hole in the Kaluza-Klein spacetime with the matched asymptotic expansion method. The corrections to the thermodynamic variables are calculated up to the post-Newtonian order. We confirmed that the method can work very well in the Einstein-Maxwell theory. 
Ryotaku Suzuki, Shunichiro Kinoshita and Tetsuya Shiromizu
hep-th gr-qc