Hyperplane-Symmetric Static Einstein-Dirac Spacetime
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909338202800128 |
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| author | Schliemann, John Sonnleitner, Tim |
| author_facet | Schliemann, John Sonnleitner, Tim |
| contents | We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field couples via the Einstein equations to spacetime, and in the massless case the Dirac field is required to fulfill appropriate constraints in order to eliminate off-diagonal components of the energy-momentum tensor. We also give explicit expressions for curvature invariants including the Ricci scalar and the Kretschmann scalar, indicating physical singularities. Moreover, we reduce the general solution of the geodesic equation to quadratures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperplane-Symmetric Static Einstein-Dirac Spacetime Schliemann, John Sonnleitner, Tim General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field couples via the Einstein equations to spacetime, and in the massless case the Dirac field is required to fulfill appropriate constraints in order to eliminate off-diagonal components of the energy-momentum tensor. We also give explicit expressions for curvature invariants including the Ricci scalar and the Kretschmann scalar, indicating physical singularities. Moreover, we reduce the general solution of the geodesic equation to quadratures. |
| title | Hyperplane-Symmetric Static Einstein-Dirac Spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2410.04582 |