Stability and rigidity of axisymmetric marginally outer trapped two-spheres
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908628031635456 |
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| author | Galloway, Gregory J. Mendes, Abraão |
| author_facet | Galloway, Gregory J. Mendes, Abraão |
| contents | In [7], H. Bray, S. Brendle, and A. Neves studied rigidity properties of area-minimizing two-spheres in Riemannian three-manifolds with uniformly positive scalar curvature. In [13], these results were extended to marginally outer trapped surfaces (MOTS) in general initial data sets $(M^3,g,K)$ under a natural energy condition. In the present work, we refine the latter results to the setting of axisymmetric MOTS in initial data sets admitting a nontrivial Killing vector field. Conditions for the stability of such MOTS, as well as a new foliation lemma by axisymmetric surfaces of constant outward null expansion, are obtained. Finally, we discuss some aspects of the rotating Nariai spacetimes and their relation to these results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and rigidity of axisymmetric marginally outer trapped two-spheres Galloway, Gregory J. Mendes, Abraão Differential Geometry General Relativity and Quantum Cosmology In [7], H. Bray, S. Brendle, and A. Neves studied rigidity properties of area-minimizing two-spheres in Riemannian three-manifolds with uniformly positive scalar curvature. In [13], these results were extended to marginally outer trapped surfaces (MOTS) in general initial data sets $(M^3,g,K)$ under a natural energy condition. In the present work, we refine the latter results to the setting of axisymmetric MOTS in initial data sets admitting a nontrivial Killing vector field. Conditions for the stability of such MOTS, as well as a new foliation lemma by axisymmetric surfaces of constant outward null expansion, are obtained. Finally, we discuss some aspects of the rotating Nariai spacetimes and their relation to these results. |
| title | Stability and rigidity of axisymmetric marginally outer trapped two-spheres |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.02480 |