Cylindrical symmetry locally isometric $AdS_{4}$ spacetime

TL;DR

This paper introduces a new maximally symmetric vacuum spacetime that is locally isometric to anti-de Sitter space, features closed timelike curves, and extends the properties of Misner space into four dimensions.

Contribution

It presents a regular, singularity-free 4D spacetime with causality-violating properties, expanding the understanding of time-machine solutions in curved spacetime.

Findings

Spacetime admits closed timelike curves after a certain time

The spacetime is free of curvature singularities

It extends Misner space properties to four dimensions

Abstract

We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from curvature singularities and an $4D$ extension of the Misner space in curved spacetime with identical causality violating properties.