A note on geodesic connectedness of G\"odel type spacetimes

TL;DR

This paper investigates the geodesic connectedness of G"odel type spacetimes by linking it to critical points of a functional, and improves existing results using known static spacetime analysis techniques.

Contribution

It reduces the problem of geodesic connectedness in G"odel type spacetimes to a functional analysis problem and enhances previous findings with established static spacetime results.

Findings

Reduced geodesic connectedness problem to functional critical points

Improved previous results on G"odel type spacetimes

Connected static spacetime analysis to G"odel spacetime properties

Abstract

In this note we reduce the problem of geodesic connectedness in a wide class of G\"odel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former.