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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02301 |
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| _version_ | 1866912410906918912 |
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| author | Boos, Jens |
| author_facet | Boos, Jens |
| contents | We consider the autoparallel motion of test bodies in static, spherically symmetric spacetimes with torsion. We prove complete integrability of such motion for a wide range of off-shell geometries via four commuting autoparallel Killing vectors. Since these vectors reduce to translation generators in a certain limit, we refer to these geometries as `translation invariant.' Invoking the field equations of quadratic Poincaré gauge gravity we re-derive an exact Schwarzschild black hole solution endowed with a non-trivial torsion field scaling as $GM/r^2$, where $M$ denotes the ADM mass of the black hole. Studying the qualitative orbital dynamics via effective potentials we find notable discrepancies between autoparallels (straightest possible paths) and geodesics (shortest possible paths). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | `Translation invariant' black hole: autoparallels and complete integrability Boos, Jens General Relativity and Quantum Cosmology We consider the autoparallel motion of test bodies in static, spherically symmetric spacetimes with torsion. We prove complete integrability of such motion for a wide range of off-shell geometries via four commuting autoparallel Killing vectors. Since these vectors reduce to translation generators in a certain limit, we refer to these geometries as `translation invariant.' Invoking the field equations of quadratic Poincaré gauge gravity we re-derive an exact Schwarzschild black hole solution endowed with a non-trivial torsion field scaling as $GM/r^2$, where $M$ denotes the ADM mass of the black hole. Studying the qualitative orbital dynamics via effective potentials we find notable discrepancies between autoparallels (straightest possible paths) and geodesics (shortest possible paths). |
| title | `Translation invariant' black hole: autoparallels and complete integrability |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.02301 |