Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes

TL;DR

This paper proves a classical area theorem for dynamical wormholes and black holes, demonstrating that the maximal cross-sectional area remains invariant under general classical evolution, thus providing a gravitational dual to quantum entanglement conservation.

Contribution

It introduces a new classical area theorem for wormholes and black holes that models entanglement conservation in the ER=EPR framework.

Findings

Maximin area for horizons is invariant under classical evolution.

The theorem applies to dynamical wormholes with horizon mergers.

It characterizes ER=EPR duality in the classical limit.

Abstract

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.