Speaker Marcelo Rubio (Sissa,Trieste)
Title: 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.