Holographic Rényi entropy and generalized entropy method

In this paper we use the method of generalized gravitational entropy in [6] 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 being closely related to that in [4]. For a general entangling surface we derive the area law of entanglement entropy. The area law is closely related to the local property of the entangling surface.