Global stability of ghostly field theories: Classical scattering in $(N+1)$ dimensions

Abstract

We review results on small-data global stability and highlight their applicability to classical interacting scalar fields with opposite-sign kinetic terms (ghosts). Further, we present a one-parameter family of numerical scattering solutions under the simplifying assumption of spherical symmetry. We thereby identify classical ghostly field theories with polynomial interaction potentials for which small-data global stability apparently extends to large-data global stability, i.e., global stability for all compactly supported initial data. These global stability results support an underlying physical mechanism by which the ghost instability can be quenched due to dominant self-interactions, at least in classical physics.

21 pages, 6 figures, and 1 appendix and references; source code available under https://github.com/aaron-hd/ghostlyPDE_spherical.git animations available under https://zenodo.org/records/17178254