Towards hyperboloidal Numerical Relativity in Generalized Harmonic Gauge

Abstract:

The use of hyperboloidal coordinates in the numerical evolution of hyperbolic Partial Differential Equations promise a clean capture of the radiation signal asymptotically. Although mathematically appealing, a fully satisfactory application of such methods in Numerical Relativity has not been achieved yet.

One key difficulty is subtle interplay between the decay of the evolved fields and divergent terms appearing from the use of a compactified domain.
In this talk I will present the numerical results of the recently understood asymptotic properties of the Generalized Harmonic Formulation of General Relativity for some choice of gauge and metric functions.

In particular, I will discuss 3+1-dimensional evolution of a simplified model with the same asymptotics, as well as full non-linear General Relativity evolutions under the assumption of spherical symmetry. These works are steps towards applying hyperboloidal methods in full Numerical Relativity without symmetry assumptions, which could improve the Gravitational Wave extraction procedure significantly.