# From black hole entropy to energy-minimizing states in QFT

## 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 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.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

- OSTI Identifier:
- 1597547

- Alternate Identifier(s):
- OSTI ID: 1737600

- Grant/Contract Number:
- AC02-05CH11231; SC0019380; PHY-1820912

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; gauge-gravity dualities

### Citation Formats

```
Bousso, Raphael, Chandrasekaran, Venkatesa, and Shahbazi-Moghaddam, Arvin. From black hole entropy to energy-minimizing states in QFT. United States: N. p., 2020.
Web. doi:10.1103/physrevd.101.046001.
```

```
Bousso, Raphael, Chandrasekaran, Venkatesa, & Shahbazi-Moghaddam, Arvin. From black hole entropy to energy-minimizing states in QFT. United States. doi:10.1103/physrevd.101.046001.
```

```
Bousso, Raphael, Chandrasekaran, Venkatesa, and Shahbazi-Moghaddam, Arvin. Wed .
"From black hole entropy to energy-minimizing states in QFT". United States. doi:10.1103/physrevd.101.046001.
```

```
@article{osti_1597547,
```

title = {From black hole entropy to energy-minimizing states in QFT},

author = {Bousso, Raphael and Chandrasekaran, Venkatesa and Shahbazi-Moghaddam, Arvin},

abstractNote = {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 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.},

doi = {10.1103/physrevd.101.046001},

journal = {Physical Review D},

number = 4,

volume = 101,

place = {United States},

year = {2020},

month = {2}

}

DOI: 10.1103/physrevd.101.046001

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