Numerical evolution of well-posed field theories with anisotropic scaling

Event type
Event date
On-site: Room TBD
Marcelo Rubio (SISSA, Trieste)
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 novel 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.