# Analysis of geometries with closed timelike curves - General Relativity and Quantum Cosmology

Abstract: This work deals with the analysis of cylindrically symmetric and stationaryspace-times $\mathcal{C} {t}$ with closed timelike curves. The equation ofmotion describing the evolution of a massive scalar field in a$\mathcal{C} {t}$ space-time is obtained. A class of space-times with closedtimelike curves describing cosmic strings and cylinders is studied in detail.In such space-times, both massive particles as well as photons can reach thenon-causal region. Geodesics and closed timelike curves are calculated andinvestigated. 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 futureand past inside the non-causal region. Exact solutions for the equation ofmotion of massive scalar field propagating in cosmic strings and cylinderspace-times are presented. Quasinormal modes for the scalar field have beencalculated in static and rotating cosmic cylinders. We found unstable modes inthe rotating cases. Rotating as well as static cosmic strings, i.e., withoutregular interior solutions, do not display quasinormal modes for the scalarfield. We conclude presenting a conjecture relating closed timelike curves andspace-time instability.

Author: A. B. Pavan

Source: https://arxiv.org/