Numerical evolution of well-posed field theories with anisotropic scaling

ABSTRACT: Dynamical equations exhibiting an anisotropic scaling between space and time admit a dispersive nature, as they contain higher-order spatial derivatives, but remain second order in time. This is the case of a class of Lorentz-violating theories of gravity, and this feature results inconvenient for performing long-time numerical evolutions with standard explicit schemes.

In this talk I will introduce a nobel scheme which is implicit, stable and second-order accurate, for sufficiently large time steps. As a proof of concept, we will apply it for evolving the Lifshitz scalar field on top of a spherically symmetric black hole space-time. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.