Aspects of the geometry and topology of expanding horizons
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| Title: | Aspects of the geometry and topology of expanding horizons |
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| Authors: | Galloway, Gregory J., Mendes, Abraão |
| Source: | Proceedings of the American Mathematical Society. 153:1239-1250 |
| Publication Status: | Preprint |
| Publisher Information: | American Mathematical Society (AMS), 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Mathematics - Differential Geometry, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Differential Geometry (math.DG), Global submanifolds, FOS: Mathematics, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), marginally trapped surfaces, initial data sets, General Relativity and Quantum Cosmology, Geometric evolution equations |
| Description: | The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of g \mathfrak {g} -stability for a general closed hypersurface Σ \Sigma in an ambient initial data set and prove that, under natural energy conditions, Σ \Sigma has positive Yamabe type, that is, Σ \Sigma admits a metric of positive scalar curvature, provided Σ \Sigma is g \mathfrak {g} -stable. A similar result is obtained when Σ \Sigma is embedded in a null hypersurface of a spacetime satisfying the dominant energy condition. Area bounds under similar conditions are obtained in the case where Σ \Sigma is 2 2 -dimensional. Conditions implying g \mathfrak {g} -stability are also discussed. Finally, we obtain a spacetime positive mass theorem for initial data sets with compact boundary Σ \Sigma of positive null expansion, assuming that the dominant energy condition is sufficiently strict near Σ \Sigma . This extends recent results of Galloway-Lee and Lee-Lesourd-Unger. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/17092 |
| DOI: | 10.48550/arxiv.2404.02019 |
| Access URL: | http://arxiv.org/abs/2404.02019 https://zbmath.org/7983020 https://doi.org/10.1090/proc/17092 |
| Rights: | arXiv Non-Exclusive Distribution URL: https://www.ams.org/publications/copyright-and-permissions |
| Accession Number: | edsair.doi.dedup.....dd33556d25a90b61be2a5436b116434e |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of g \mathfrak {g} -stability for a general closed hypersurface Σ \Sigma in an ambient initial data set and prove that, under natural energy conditions, Σ \Sigma has positive Yamabe type, that is, Σ \Sigma admits a metric of positive scalar curvature, provided Σ \Sigma is g \mathfrak {g} -stable. A similar result is obtained when Σ \Sigma is embedded in a null hypersurface of a spacetime satisfying the dominant energy condition. Area bounds under similar conditions are obtained in the case where Σ \Sigma is 2 2 -dimensional. Conditions implying g \mathfrak {g} -stability are also discussed. Finally, we obtain a spacetime positive mass theorem for initial data sets with compact boundary Σ \Sigma of positive null expansion, assuming that the dominant energy condition is sufficiently strict near Σ \Sigma . This extends recent results of Galloway-Lee and Lee-Lesourd-Unger. |
|---|---|
| ISSN: | 10886826 00029939 |
| DOI: | 10.1090/proc/17092 |