Analysis of geometries with closed timelike curves

TL;DR

This paper analyzes space-times with closed timelike curves, studying particle and photon trajectories, scalar field equations, and quasinormal modes, revealing instabilities especially in rotating cosmic cylinders and proposing a link between CTCs and space-time instability.

Contribution

It provides a detailed analysis of geodesics, scalar field dynamics, and quasinormal modes in space-times with CTCs, including new solutions and the relation to stability.

Findings

Massive particles and photons exhibit confined and scattering trajectories.

Unstable quasinormal modes are found in rotating cosmic cylinders.

Static and rotating cosmic strings without interior solutions lack quasinormal modes.

Abstract

This work deals with the analysis of cylindrically symmetric and stationary space-times $\mathcal{C}_{t}$ with closed timelike curves. The equation of motion describing the evolution of a massive scalar field in a $\mathcal{C}_{t}$ space-time is obtained. A class of space-times with closed timelike curves describing cosmic strings and cylinders is studied in detail. In such space-times, both massive particles as well as photons can reach the non-causal region. Geodesics and closed timelike curves are calculated and investigated. We have observed that massive particles and photons describe, essentially, two kinds of trajectories: confined orbits and scattering states. The analysis of the light cones show us clearly the intersection between future and past inside the non-causal region. Exact solutions for the equation of motion of massive scalar field propagating in cosmic strings and cylinder space-times are presented. Quasinormal modes for the scalar field have been calculated in static and rotating cosmic cylinders. We found unstable modes in the rotating cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal modes for the scalar field. We conclude presenting a conjecture relating closed timelike curves and space-time instability.