On shape dependence of holographic entanglement entropy in AdS4/CFT3

Understand

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds.

• Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes.
• The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly.
• When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space.