Nonlinear constraints on gravity from entanglement

TL;DR

This paper derives nonlinear constraints on gravitational theories using entanglement entropy positivity, showing Einstein gravity satisfies these constraints while others are restricted.

Contribution

It introduces a method to obtain nonlinear gravitational constraints from entanglement entropy positivity using the Ryu-Takayanagi formula and derivative expansion techniques.

Findings

Einstein gravity satisfies the derived positivity constraints.

Non-Einstein theories are constrained away from the Einstein point.

A Green's function for first-order entanglement corrections was computed.

Abstract

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.