Geometric structure of Galilean spacetimes admitting a conformally Leibnizian vector field

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 vector fields whose flow generates conformal transformations of the Leibnizian structure, particularly highlighting torse-forming, 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. In particular, natural conditions are given to characterize the geometric structure as Galilean Generalized Robertson-Walker and Galilean Twisted spacetimes, as well as to prove uniqueness splitting results.