On Twisted Spacetimes: a new class of Galilean cosmological models

TL;DR

This paper introduces Galilean Twisted spacetimes within the generalized Newton-Cartan framework, establishing their structure, global properties, and geodesic completeness, thus expanding the class of cosmological models in non-relativistic gravity.

Contribution

It defines Galilean Twisted spacetimes as duals to relativistic models and explores their global structure and completeness properties, a novel extension in Newton-Cartan theory.

Findings

Galilean Twisted spacetimes are characterized by local structure with a timelike torqued vector field.

Global splitting results confirm these spacetimes can be globally decomposed as Twisted spacetimes.

Conditions for geodesic and free-falling observer completeness are established.

Abstract

Within the generalized Newton-Cartan theory, Galilean Twisted spacetimes are introduced as dual models of the well-known relativistic twisted spacetimes. As a natural generalization, torqued vector fields in Galilean spacetimes are defined, showing that the local structure of a Galilean spacetime admitting a timelike torqued vector field is given by a Twisted spacetime. In addition, several results assuring the global splitting as Twisted spacetime are obtained. On the other hand, completeness of free falling observers is studied, as well as general geodesic completeness.