# Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT

## TL;DR

This paper extends a coarse-graining approach to semiclassical gravity to explain black hole entropy and minimum energy states in quantum field theory, providing new insights into gravitational and nongravitational limits.

## Contribution

It generalizes the Engelhardt-Wall coarse-graining construction to semiclassical gravity and verifies its implications in a nongravitational limit, supporting Wall’s ant conjecture.

## Key findings

- The construction exists classically but fails with Null Energy Condition violation.
- The proposal implies minimum energy states are localized as shocks.
- The properties hold in explicit nongravitational limit construction.

## Abstract

Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining Bekenstein-Hawking entropy as a coarse-grained entropy. The construction can be proven to exist classically but fails if the Null Energy Condition is violated. Here we extend the coarse-graining construction to semiclassical gravity. Its validity is conjectural, but we are able to extract an interesting nongravitational limit. Our proposal implies Wall's ant conjecture on the minimum energy of a completion of a quantum field theory state on a half-space. It further constrains the properties of the minimum energy state; for example, the minimum completion energy must be localized as a shock at the cut. We verify that the predicted properties hold in a recent explicit construction of Ceyhan and Faulkner, which proves our conjecture in the nongravitational limit.