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August 19, 2025Physica Scripta0 citations

Geometric structure of Galilean spacetimes admitting a conformally Leibnizian vector field.

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DFDaniel de la FuenteRRRafael M. RubioJTJose Torrente Teruel

Key Points

  • Galilean spacetimes exhibit unique structures through conformally Leibnizian vector fields, enhancing geometric understanding.
  • These vector fields enable local and potentially global spacetime splits via Galilean products, indicating rich geometric complexity.
  • The paper highlights key transformational features of vector fields, focusing on torseforming, torque, and concircular types.
  • Insights into irrotational fields of observers within the same gravitational field underscore the study's implications for spacetime geometry.

Abstract

Abstract In this paper we study the geometric structure of Galilean spacetimes that possess a certain type of infinitesimal symmetries. Specifically, we assume the existence of certain vector fields whose flow generates conformal transformations of the Leibnizian structure, particularly highlighting torseforming, torque, and concircular vector fields. Such fields enable a local splitting of spacetime as a Galilean product, which, under certain additional hypotheses, can be extended to a global one. Finally, we delve deeper into the analysis of the multiplicity of irrotational conformally Leibnizian fields of observers with the same gravitational field.

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Cite This Study

Fuente et al. (2025) studied this question.

synapsesocial.com/papers/68af4959ad7bf08b1ead54e4https://doi.org/10.1088/1402-4896/adfd20
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