Physical Process Version of the First Law of Thermodynamics for Black   Holes in Higher Dimensional Gravity
  The problem of physical process version of the first law of black hole thermodynamics for charged rotating black hole in n-dimensional gravity is elaborated. The formulae for the first order variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory are derived. These variations are expressed by means of the perturbed matter energy momentum tensor and matter current density. 
Marek Rogatko