Nonlinear constraints on gravity from entanglement

Understand

Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual.

• We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion.
• We show that the Einstein value satisfies the positivity condition while the multi-dimensional parameter space away from it gets constrained.