Stability of Closed Timelike Curves in a Galileon Model

TL;DR

This paper investigates the stability of closed timelike curves in a Galileon model with multiple metrics, finding that small perturbations do not grow, indicating local stability despite global pathologies.

Contribution

It provides an explicit analysis of perturbations around CTC solutions in a Galileon model, demonstrating local stability in the presence of global CTC pathologies.

Findings

Small, short-wavelength perturbations do not grow over time.

Global CTCs lead to nonlocal constraints on initial data.

Locally, the solutions are stable against perturbations.

Abstract

Recently Burrage, de Rham, Heisenberg and Tolley have constructed eternal, classical solutions with closed timelike curves (CTCs) in a Galileon model coupled to an auxiliary scalar field. These theories contain at least two distinct metrics and, in configurations with CTCs, two distinct notions of locality. As usual, globally CTCs lead to pathologies including nonlocal constraints on the initial Cauchy data. Locally, with respect to the gravitational metric, we use a WKB approximation to explicitly construct small, short-wavelength perturbations without imposing the nonlocal constraints and observe that these perturbations do not grow and so do not lead to an instability.