Teleparallel formalism of galilean gravity

TL;DR

This paper develops a teleparallel formalism for galilean gravity using a 5-bein and torsion in a (4+1)D manifold, applying it to spherically symmetric solutions and coupling to Dirac fields.

Contribution

It introduces a novel galilean teleparallel gravity framework based on a pseudo-Riemannian manifold with light-cone coordinates.

Findings

Derived two spherically symmetric solutions, including a Schwarzschild-like ansatz.

Established a method to couple 5-bein fields to galilean covariant Dirac fields.

Abstract

A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.