Abstract
In this paper we use the method of generalized gravitational entropy in \cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical entangling surface, and calculate the Rényi entropy with the dual bulk gravity theory being either Einstein gravity or Lovelock gravity, this approach is closely related to that in \cite{Casini:2011kv}. For a general entangling surface we derive the area law of entanglement entropy. The area law is closely related with the local property of the entangling surface.
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