A Type D Non-Vacuum Spacetime with Causality Violating Curves, and its Physical Interpretation

TL;DR

This paper introduces a regular, non-vacuum, type D spacetime solution with causality-violating closed timelike curves, stable under perturbations, and provides a physical interpretation based on geodesic deviation analysis.

Contribution

It presents a novel, topologically trivial, non-vacuum solution with causality violation and analyzes its physical implications and stability properties.

Findings

Existence of stable closed timelike curves beyond the null curve

The spacetime admits non-closed null geodesics

Stress-energy tensor satisfies various energy conditions

Abstract

We present a topologically trivial, non-vacuum solution of the Einstein's field equations in four-dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid $p=\omega\,\rho$. The metric admits a twisting, shearfree, non-exapnding timelike geodesic congruence. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.