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`Translation invariant' black hole: autoparallels and complete integrability

2025/06/02 by Jens Boos, Boos, Jens
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2506.02301

openalex publication_date 2025/06/02 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

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/r2, 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).

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