Approximations of the quasi-local Bartnik mass in general relativity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910370651701248 |
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| author | Escobar-Diaz, Leon Stevens, Chris |
| author_facet | Escobar-Diaz, Leon Stevens, Chris |
| contents | In this study, we employ eth-operators and spin-weighted spherical harmonics to express the ADM mass of a static space-time based on the mean values of its components over a a radius-$r$ sphere. While initially derived for standard spherical coordinates, we showcase its adaptability by demonstrating its usefulness in expressing a quasilocal mass; specifically, the Bartnik mass, of an almost round 2D-hypersurface in terms of some specific boundary conditions. Additionally, we utilize this formulation to propose a deep learning methodology for numerically constructing static metrics that incorporate 2D-hypersurfaces with specified Bartnik mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximations of the quasi-local Bartnik mass in general relativity Escobar-Diaz, Leon Stevens, Chris General Relativity and Quantum Cosmology In this study, we employ eth-operators and spin-weighted spherical harmonics to express the ADM mass of a static space-time based on the mean values of its components over a a radius-$r$ sphere. While initially derived for standard spherical coordinates, we showcase its adaptability by demonstrating its usefulness in expressing a quasilocal mass; specifically, the Bartnik mass, of an almost round 2D-hypersurface in terms of some specific boundary conditions. Additionally, we utilize this formulation to propose a deep learning methodology for numerically constructing static metrics that incorporate 2D-hypersurfaces with specified Bartnik mass. |
| title | Approximations of the quasi-local Bartnik mass in general relativity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2403.11372 |