Towards 3D free hyperboloidal evolution

by Dr Alex Vano-Vinuales (CENTRA, University of Lisbon)

Wednesday 30 Nov 2022, 10:00 → 12:00 Europe/Berlin

HS-5 Abbeanum (TPI, FSU Jena)

Gravitational wave radiation, our window for probing the strong field and dynamical regime of gravity, is unambiguously defined only at future infinity - the location in spacetime where light rays arrive and thus where signals and global properties of spacetimes can be measured. A convenient way to include it in numerical relativity simulations is by means of hyperboloidal foliations, which consist of smooth spacelike slices that reach future null infinity. I will review the current state of the art of two suitable free-evolution approaches. The first one uses conformal compactification, based on an idea by Nobel-laureate Roger Penrose, and implements it via the BSSN and Z4 formulations of the Einstein equations. It has provided very promising spherically symmetric numerical evolutions of a massless scalar field coupled to gravity, which I will show. The second approach employs the dual-frame method to preserve the well-posedness of the Generalized Harmonic Gauge formulation while using coordinates adapted to the hyperboloidal slices. Its preliminary results in spherical symmetry also show the potential of this approach. Finally, I will give an update on current ongoing work towards 3D, as the final goal of this work is to provide a far-field numerical framework that includes null infinity for simulations of compact object mergers with accurate gravitational wave extraction.