Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913794608857088 |
|---|---|
| author | Allen, Brian Bryden, Edward Kazaras, Demetre Khuri, Marcus |
| author_facet | Allen, Brian Bryden, Edward Kazaras, Demetre Khuri, Marcus |
| contents | We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. More precisely, the lower bound consists of a universal constant multiplied by the square root of the minimal area required to enclose the outermost apparent horizon. Here the outermost apparent horizon may contain both marginally outer trapped (MOTS) and marginally inner trapped (MITS) components. The proof is based on the harmonic level set approach to the positive mass theorem, combined with the Jang equation and techniques arising from the stability argument of Dong-Song \cite{Dong-Song}. As a corollary, we also obtain a version of the Penrose inequality for 3-dimensional asymptotically hyperbolic Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes Allen, Brian Bryden, Edward Kazaras, Demetre Khuri, Marcus Differential Geometry General Relativity and Quantum Cosmology 53C21, 83C57, 83C75 We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. More precisely, the lower bound consists of a universal constant multiplied by the square root of the minimal area required to enclose the outermost apparent horizon. Here the outermost apparent horizon may contain both marginally outer trapped (MOTS) and marginally inner trapped (MITS) components. The proof is based on the harmonic level set approach to the positive mass theorem, combined with the Jang equation and techniques arising from the stability argument of Dong-Song \cite{Dong-Song}. As a corollary, we also obtain a version of the Penrose inequality for 3-dimensional asymptotically hyperbolic Riemannian manifolds. |
| title | Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53C21, 83C57, 83C75 |
| url | https://arxiv.org/abs/2504.10641 |