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Paper   IPM / Physic / 8597
School of Physics
  Title:   Double-Horizon Limit, AdS Geometry and Entropy Function
1.  H. Arfaei
2.  R. Fareghbal
  Status:   Published
  Journal: Nucl. Phys. B
  Vol.:  802
  Year:  2008
  Pages:   405
  Supported by:  IPM
By starting from a generic metric which describes four dimensional stationary black holes in an arbitrary theory of gravity , we show that the AdS near horizon geometry is a consequence of finiteness and double-horizon limit. For the neutral and electrically charged rotating black holes in some theories of gravity such as f(R) gravity which are described by this general metric , we show that applying this limit in the equations of motion results a set of decoupled equations at the horizon which can be solved and give the near horizon parameters. It is shown that these decoupled equations come from variation of a function like entropy function which is evaluated at the horizon by imposing double-horizon limit and without going to the near-horizon coordinate. We simplify Wald formula at the horizon by using this limit and get the results similar to the entropy function method.

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