Exact differential and corrected area law for stationary black holes in tunneling method

@article{Banerjee2009ExactDA,
  title={Exact differential and corrected area law for stationary black holes in tunneling method},
  author={Rabin Banerjee and Sujoy Kumar Modak},
  journal={Journal of High Energy Physics},
  year={2009},
  volume={2009},
  pages={063-063}
}
We give a new and conceptually simple approach to obtain the ``first law of black hole thermodynamics'' from a basic thermodynamical property that entropy (S) for any stationary black hole is a state function implying that dS must be an exact differential. Using this property we obtain some conditions which are analogous to Maxwell's relations in ordinary thermodynamics. From these conditions we are able to explicitly calculate the semiclassical Bekenstein-Hawking entropy, considering the most… 
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