  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.
