Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in   Einstein-Maxwell Theory
  We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole. 
Sayantani Bhattacharyya, Binata Panda and Ashoke Sen
hep-th gr-qc