Quantum Information Bound on the Energy

TL;DR

This paper proposes a quantum version of the Penrose inequality using generalized entropy, demonstrating violations at the semiclassical level and exploring implications for cosmic censorship.

Contribution

It introduces a Quantum Penrose Inequality replacing area with generalized entropy and tests its validity against classical expectations.

Findings

Quantum states violate the classical Penrose inequality.

The generalized entropy-based inequality holds under certain conditions.

Implications for weak cosmic censorship are discussed.

Abstract

According to the classical Penrose inequality, the mass at spatial infinity is bounded from below by a function of the area of certain trapped surfaces. We exhibit quantum field theory states that violate this relation at the semiclassical level. We formulate a Quantum Penrose Inequality, by replacing the area with the generalized entropy of the lightsheet of an appropriate quantum trapped surface. We perform a number of nontrivial tests of our proposal, and we consider and rule out alternative formulations. We also discuss the relation to weak cosmic censorhip.