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Paper IPM / P / 8597  


Abstract:  
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 doublehorizon 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 doublehorizon limit and
without going to the nearhorizon 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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