# Energy conditions and junction conditions

## Abstract

We consider the familiar junction conditions described by Israel for thin timelike walls in Einstein-Hilbert gravity. One such condition requires the induced metric to be continuous across the wall. Now, there are many spacetimes with sources confined to a thin wall for which this condition is violated and the Israel formalism does not apply. However, we explore the conjecture that the induced metric is in fact continuous for any thin wall which models spacetimes containing only positive energy matter. Thus, the usual junction conditions would hold for all positive energy spacetimes. This conjecture is proven in various special cases, including the case of static spacetimes with spherical or planar symmetry as well as settings without symmetry which may be sufficiently well approximated by smooth spacetimes with well-behaved null geodesic congruences.

- Authors:

- Physics Department, UCSB, Santa Barbara, California 93106 (United States) and Perimeter Institute, 31 Caroline St. N, Waterloo, Ontario N2L 2Y5 (Canada)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20711351

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.72.044016; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; DIFFERENTIAL GEOMETRY; GENERAL RELATIVITY THEORY; GRAVITATION; MATTER; SPACE-TIME; SPHERICAL CONFIGURATION; SYMMETRY

### Citation Formats

```
Marolf, Donald, Yaida, Sho, and Mathematics Department, UCSB, Santa Barbara, California 93106.
```*Energy conditions and junction conditions*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.044016.

```
Marolf, Donald, Yaida, Sho, & Mathematics Department, UCSB, Santa Barbara, California 93106.
```*Energy conditions and junction conditions*. United States. doi:10.1103/PhysRevD.72.044016.

```
Marolf, Donald, Yaida, Sho, and Mathematics Department, UCSB, Santa Barbara, California 93106. Mon .
"Energy conditions and junction conditions". United States. doi:10.1103/PhysRevD.72.044016.
```

```
@article{osti_20711351,
```

title = {Energy conditions and junction conditions},

author = {Marolf, Donald and Yaida, Sho and Mathematics Department, UCSB, Santa Barbara, California 93106},

abstractNote = {We consider the familiar junction conditions described by Israel for thin timelike walls in Einstein-Hilbert gravity. One such condition requires the induced metric to be continuous across the wall. Now, there are many spacetimes with sources confined to a thin wall for which this condition is violated and the Israel formalism does not apply. However, we explore the conjecture that the induced metric is in fact continuous for any thin wall which models spacetimes containing only positive energy matter. Thus, the usual junction conditions would hold for all positive energy spacetimes. This conjecture is proven in various special cases, including the case of static spacetimes with spherical or planar symmetry as well as settings without symmetry which may be sufficiently well approximated by smooth spacetimes with well-behaved null geodesic congruences.},

doi = {10.1103/PhysRevD.72.044016},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 72,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2005},

month = {Mon Aug 15 00:00:00 EDT 2005}

}