Zero Energy Configurations in General Relativity

Abstract

We investigate the ratio of gravitational binding energy to rest mass in general relativity. For N pointlike masses, an upper bound on the magnitude of this ratio can be derived using the second law of black hole dynamics. Only as N approaches infinity can it approach one. A configuration that saturates the $N = \infty$ bound is a thin spherical shell as its radius is taken to zero. This system provides, in principle, a perfectly efficient mechanism for converting rest mass into energy. We mention possible implications for the black hole information problem.