Entanglement equilibrium for higher order gravity

TL;DR

This paper demonstrates that linearized higher derivative gravity equations correspond to an entanglement entropy equilibrium condition in small spherical regions, extending Jacobson's derivation of Einstein's equations to include higher curvature corrections.

Contribution

It introduces a generalized volume functional and relates higher derivative gravitational field equations to entanglement entropy variations, expanding the entanglement equilibrium framework.

Findings

Linearized higher derivative equations are equivalent to entanglement entropy equilibrium.

Introduces the generalized volume functional related to higher curvature corrections.

Establishes a connection between field equations and entanglement in maximally symmetric spacetimes.

Abstract

We show that the linearized higher derivative gravitational field equations are equivalent to an equilibrium condition on the entanglement entropy of small spherical regions in vacuum. This extends Jacobson's recent derivation of the Einstein equation using entanglement to include general higher derivative corrections. The corrections are naturally associated with the subleading divergences in the entanglement entropy, which take the form of a Wald entropy evaluated on the entangling surface. Variations of this Wald entropy are related to the field equations through an identity for causal diamonds in maximally symmetric spacetimes, which we derive for arbitrary higher derivative theories. If the variations are taken holding fixed a geometric functional that we call the generalized volume, the identity becomes an equivalence between the linearized constraints and the entanglement equilibrium condition. We note that the fully nonlinear higher curvature equations cannot be derived from the linearized equations applied to small balls, in contrast to the situation encountered in Einstein gravity. The generalized volume is a novel result of this work, and we speculate on its thermodynamic role in the first law of causal diamond mechanics, as well as its possible application to holographic complexity.