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

### APA

Shahbazi-Moghaddam, A. (2019). Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT. Perimeter Institute. https://pirsa.org/19100040

### MLA

Shahbazi-Moghaddam, Arvin. Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT. Perimeter Institute, Oct. 29, 2019, https://pirsa.org/19100040

### BibTex

@misc{ pirsa_19100040, doi = {}, url = {https://pirsa.org/19100040}, author = {Shahbazi-Moghaddam, Arvin}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT}, publisher = {Perimeter Institute}, year = {2019}, month = {oct}, note = {PIRSA:19100040 see, \url{https://pirsa.org}} }

## 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 the 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 halfspace. 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.