Comparison of Vacuum Static Quadrupolar Metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866916650357358592 |
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| author | Frutos-Alfaro, Francisco Quevedo, Hernando Sánchez, Pedro |
| author_facet | Frutos-Alfaro, Francisco Quevedo, Hernando Sánchez, Pedro |
| contents | We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analyzing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the $q-$metric, a variant of the Zipoy-Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_06734 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Comparison of Vacuum Static Quadrupolar Metrics Frutos-Alfaro, Francisco Quevedo, Hernando Sánchez, Pedro General Relativity and Quantum Cosmology We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analyzing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the $q-$metric, a variant of the Zipoy-Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter. |
| title | Comparison of Vacuum Static Quadrupolar Metrics |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/1704.06734 |