Physical and Stable Closed Timelike Curves

TL;DR

This paper presents a class of stable, flat spacetime models with closed timelike curves (CTCs) constructed via a compactified extra dimension, avoiding common pathologies and ensuring classical stability and energy conservation.

Contribution

It introduces a novel class of CTC solutions using a compactified extra dimension that are stable, flat, and free of typical pathologies seen in previous models.

Findings

The constructed CTCs are stable and satisfy classical energy conditions.

The models avoid pathologies like infinite matter cylinders and negative energy distributions.

Energy is conserved along the CTCs due to stationarity.

Abstract

We construct a class of closed timelike curves (CTCs) using a compactified extra dimension $u$. A nonzero metric element $g_{tu}(u)$ enables particles to travel backwards in global time $t$. The compactified dimension guarantees that the geodesic curve closes in $u$. The effective 2D ($t$ and $u$) nature of the metric ensures that spacetime is flat, therein satisfying all the classical stability conditions as expressed by the energy conditions. Finally, stationarity of the metric guarantees that a particle's energy is conserved. The pathologies that plague many hypothesized metrics admitting CTCs, e.g. an infinite cylinder of matter, a negative energy-distribution, particle acceleration/blue-shifting along the CTC, do not occur within our metric class.