Geometric Analysis of Ori-type Spacetimes

TL;DR

This paper analyzes the geometric structure of Ori-type spacetimes, focusing on symmetries and geodesics, to understand their properties related to time machines and closed timelike curves.

Contribution

It provides a detailed geometric analysis of Ori-type spacetimes, including symmetries and geodesic behavior, with visualizations of their global structure.

Findings

Existence of closed timelike curves in Ori-type spacetimes

Identification of symmetries in these spacetimes

Insights into geodesic structure and global geometry

Abstract

In 1993 A. Ori \cite{Ori93} presented spacetimes violating the chronology condition in order to answer the question whether a time machine construction has to violate the weak energy condition or not. Later, in 2005 \cite{Ori05}, he constructed a class of time machine solutions with compact vacuum core. Both classes include an interesting global structure and it is possible to obtain closed timelike curves. Besides we focus on the geometric structure, in particular symmetries and geodesics, if feasible, and visualize several aspects.