Quantum Penrose Inequality

Abstract

The classical Penrose inequality specifies a lower bound on the total mass in terms of the area of certain trapped surfaces. This fails at the semiclassical level. We conjecture a Quantum Penrose Inequality: the mass at spatial infinity is lower-bounded by a function of the generalized entropy of the lightsheet of appropriate quantum trapped surfaces. This is the first relation between quantum information in quantum gravity, and the total energy.