Entanglement Equilibrium and the Einstein Equation.
A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA.
Ted
T
Jacobson