Energy of boundary of spacetime

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.