Time-independent wormholes

TL;DR

This paper explores static, time-independent wormholes with a unique symmetry, constructed via scalar fields with specific potentials, and analyzes their properties and boundary mutual information in the context of AdS/CFT correspondence.

Contribution

It introduces a new class of static wormhole solutions with a specific Killing symmetry, constructed with scalar domain walls, and examines their stability and boundary mutual information behavior.

Findings

Explicit examples of such wormholes in the thin wall approximation.

Solutions with exact Killing symmetry require scalar potentials that are $C^1$ but not $C^2$.

Mutual information between boundary regions is already thermalized despite interior instability.

Abstract

We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approximation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are $C^1$ but not $C^2$ and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite $t$ in the sense that they agree with the $t\rightarrow \infty$ limit of results from the familiar AdS-Kruskal solution.