Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics

TL;DR

This paper introduces a new axially symmetric vacuum solution with a cosmological constant that features a curvature singularity, closed time-like curves, and gravitational wave-like behavior on anti-de Sitter backgrounds.

Contribution

It presents a novel exact solution to Einstein's equations with unique properties, including CTCs and geodesic deviation analysis, expanding understanding of vacuum spacetimes with cosmological constant.

Findings

Presence of closed time-like curves indicating a time-machine spacetime

Solution can be interpreted as gravitational waves on anti-de Sitter space

Analysis of geodesic deviation reveals physical properties of the spacetime

Abstract

In this paper, we present a type D, non-vanishing cosmological constant, vacuum solution of the Einstein's field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial spacelike hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviation.