Journal
MODERN PHYSICS LETTERS A
Volume 35, Issue 9, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217732320500522
Keywords
Torsion; Killing theorem; modified gravity
Categories
Funding
- UNAM-DGAPA-PAPIIT [IA101818]
- CONACyT
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When spacetime torsion is present, geodesics and autoparallels generically do not coincide. In this work, the well-known method that uses Killing vectors to solve the geodesic equations is generalized for autoparallels. The main definition is that of T-Killing vectors: vector fields such that, when their index is lowered with the metric, have vanishing symmetric derivative when acted upon with a torsionful and metric-compatible derivative. The main property of T-Killing vectors is that their contraction with the autoparallels' tangents are constant along these curves. As an example, in a static and spherically symmetric situation, the autoparallel equations are reduced to an effective one-dimensional problem. Other interesting properties and extensions of T-Killing vectors are discussed.
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