Thermodynamic structure of field equations near apparent horizon for   radiating black holes
  We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity $TdS=dE+PdV$. 
Uma Papnoi, Megan Govender, Sushant G Ghosh
gr-qc