### Abstract

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2 + 1 gravity to obtain nonexistence of geons in 2 + 1 gravity. In particular, our results show that any 2 + 1 initial data set, which obeys the dominant energy condition with cosmological constant Λ ≥ 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2 + 1 gravity but also apply to quantum 2 + 1 gravity when formulated using Witten's solution space quantization.

Original language | English (US) |
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Pages (from-to) | 285-298 |

Number of pages | 14 |

Journal | Communications in Mathematical Physics |

Volume | 310 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2012 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*310*(2), 285-298. https://doi.org/10.1007/s00220-011-1396-5

**Nonexistence of Marginally Trapped Surfaces and Geons in 2 + 1 Gravity.** / Galloway, Gregory J; Schleich, Kristin; Witt, Donald M.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 310, no. 2, pp. 285-298. https://doi.org/10.1007/s00220-011-1396-5

}

TY - JOUR

T1 - Nonexistence of Marginally Trapped Surfaces and Geons in 2 + 1 Gravity

AU - Galloway, Gregory J

AU - Schleich, Kristin

AU - Witt, Donald M.

PY - 2012/3

Y1 - 2012/3

N2 - We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2 + 1 gravity to obtain nonexistence of geons in 2 + 1 gravity. In particular, our results show that any 2 + 1 initial data set, which obeys the dominant energy condition with cosmological constant Λ ≥ 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2 + 1 gravity but also apply to quantum 2 + 1 gravity when formulated using Witten's solution space quantization.

AB - We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2 + 1 gravity to obtain nonexistence of geons in 2 + 1 gravity. In particular, our results show that any 2 + 1 initial data set, which obeys the dominant energy condition with cosmological constant Λ ≥ 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2 + 1 gravity but also apply to quantum 2 + 1 gravity when formulated using Witten's solution space quantization.

UR - http://www.scopus.com/inward/record.url?scp=84857215504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857215504&partnerID=8YFLogxK

U2 - 10.1007/s00220-011-1396-5

DO - 10.1007/s00220-011-1396-5

M3 - Article

AN - SCOPUS:84857215504

VL - 310

SP - 285

EP - 298

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -