### Abstract

In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by 4π=c, where c > 0 is a lower bound on a natural energy-momentum term.We then consider the rigidity that results for stable, or weakly outermost, marginally outer trapped 2-spheres that achieve this upper bound on the area. In particular, we prove a splitting result for 3-dimensional initial data sets analogous to a result of Bray, Brendle and Neves [10] concerning area minimizing 2-spheres in Riemannian 3-manifolds with positive scalar curvature. We further show that these initial data sets locally embed as spacelike hypersurfaces into the Nariai spacetime. Connections to the Vaidya spacetime and dynamical horizons are also discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 63-83 |

Number of pages | 21 |

Journal | Communications in Analysis and Geometry |

Volume | 26 |

Issue number | 1 |

State | Published - Jan 1 2018 |

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### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty

### Cite this

*Communications in Analysis and Geometry*,

*26*(1), 63-83.

**Rigidity of marginally outer trapped 2-spheres.** / Galloway, Gregory J; Mendes, Abraão.

Research output: Contribution to journal › Article

*Communications in Analysis and Geometry*, vol. 26, no. 1, pp. 63-83.

}

TY - JOUR

T1 - Rigidity of marginally outer trapped 2-spheres

AU - Galloway, Gregory J

AU - Mendes, Abraão

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by 4π=c, where c > 0 is a lower bound on a natural energy-momentum term.We then consider the rigidity that results for stable, or weakly outermost, marginally outer trapped 2-spheres that achieve this upper bound on the area. In particular, we prove a splitting result for 3-dimensional initial data sets analogous to a result of Bray, Brendle and Neves [10] concerning area minimizing 2-spheres in Riemannian 3-manifolds with positive scalar curvature. We further show that these initial data sets locally embed as spacelike hypersurfaces into the Nariai spacetime. Connections to the Vaidya spacetime and dynamical horizons are also discussed.

AB - In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by 4π=c, where c > 0 is a lower bound on a natural energy-momentum term.We then consider the rigidity that results for stable, or weakly outermost, marginally outer trapped 2-spheres that achieve this upper bound on the area. In particular, we prove a splitting result for 3-dimensional initial data sets analogous to a result of Bray, Brendle and Neves [10] concerning area minimizing 2-spheres in Riemannian 3-manifolds with positive scalar curvature. We further show that these initial data sets locally embed as spacelike hypersurfaces into the Nariai spacetime. Connections to the Vaidya spacetime and dynamical horizons are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85041948394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041948394&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 63

EP - 83

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 1

ER -