Stability of Closed Timelike Curves in a Galileon Model

Understand

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.