Energy of boundary of spacetime

TL;DR

This paper explores how energy can be stored in the boundary of spacetime, specifically in a quantum gravitational bubble, using classical Einstein gravity and the Gibbons-Hawking-York term, revealing insights into spacetime boundaries and topological defects.

Contribution

It introduces a method to calculate boundary energy in spacetime bubbles within classical gravity, linking membrane tension to the absence of observable topological defects.

Findings

Boundary energy can be modeled with Schwarzschild metric.

Positive membrane tension explains the rarity of topological defects.

Mechanism for suppressing spacetime boundaries is proposed.

Abstract

We consider how the energy can be stored in the boundary of spacetime, in particular in a spherical bubble that can be made by a quantum gravitational process. Our calculation is performed within the framework of classical Einstein gravity by identifying the Gibbons-Hawking-York term as the membrane action. We show that the energy of the bubble can be given consistently with the Schwarzschild metric. The solution of the consistency condition suggests positive membrane tension, which explains why we do not observe such topological defects in ordinary experiences and also gives a mechanism for suppressing the spacetime with boundary in a dynamical way.