# Boundary of the future of a surface

## Abstract

We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1416867

- Alternate Identifier(s):
- OSTI ID: 1435104

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 2; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Akers, Chris, Bousso, Raphael, Halpern, Illan F., and Remmen, Grant N. Boundary of the future of a surface. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.024018.
```

```
Akers, Chris, Bousso, Raphael, Halpern, Illan F., & Remmen, Grant N. Boundary of the future of a surface. United States. doi:10.1103/PhysRevD.97.024018.
```

```
Akers, Chris, Bousso, Raphael, Halpern, Illan F., and Remmen, Grant N. Fri .
"Boundary of the future of a surface". United States. doi:10.1103/PhysRevD.97.024018.
```

```
@article{osti_1416867,
```

title = {Boundary of the future of a surface},

author = {Akers, Chris and Bousso, Raphael and Halpern, Illan F. and Remmen, Grant N.},

abstractNote = {We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.},

doi = {10.1103/PhysRevD.97.024018},

journal = {Physical Review D},

number = 2,

volume = 97,

place = {United States},

year = {2018},

month = {1}

}

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Publisher's Version of Record

DOI: 10.1103/PhysRevD.97.024018

DOI: 10.1103/PhysRevD.97.024018

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Cited by: 2 works

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Works referenced in this record:

##
Null cut loci of spacelike surfaces

journal, May 1988

- Kupeli, Demir N.
- General Relativity and Gravitation, Vol. 20, Issue 5

##
A covariant entropy conjecture

journal, July 1999

- Bousso, Raphael
- Journal of High Energy Physics, Vol. 1999, Issue 07

##
The large $N$ limit of superconformal field theories and supergravity

journal, January 1998

- Maldacena, Juan
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2

##
New Area Law in General Relativity

journal, August 2015

- Bousso, Raphael; Engelhardt, Netta
- Physical Review Letters, Vol. 115, Issue 8

##
Domain of Dependence

journal, February 1970

- Geroch, Robert
- Journal of Mathematical Physics, Vol. 11, Issue 2

##
The space-time cut locus

journal, October 1979

- Beem, John K.; Ehrlich, Paul E.
- General Relativity and Gravitation, Vol. 11, Issue 2

##
The world as a hologram

journal, November 1995

- Susskind, Leonard
- Journal of Mathematical Physics, Vol. 36, Issue 11

##
Generalized second law for cosmology

journal, January 2016

- Bousso, Raphael; Engelhardt, Netta
- Physical Review D, Vol. 93, Issue 2

##
Holography in general space-times

journal, June 1999

- Bousso, Raphael
- Journal of High Energy Physics, Vol. 1999, Issue 06

##
Proof of a new area law in general relativity

journal, August 2015

- Bousso, Raphael; Engelhardt, Netta
- Physical Review D, Vol. 92, Issue 4

##
Quantum focusing conjecture

journal, March 2016

- Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan
- Physical Review D, Vol. 93, Issue 6