Nonlinear Einstein evolution with hyperboloidal scri-fixing for gravitational-wave astronomy
Cauchy–hyperboloidal evolution of a perturbed black hole. Gold is the interface; outer boundary is at null infinity.Abstract
Gravitational radiation is naturally described at future null infinity, yet most numerical simulations evolve only a finite region of spacetime. Hyperboloidal compactification maps null infinity onto a finite grid, but applying it to Einstein’s equations introduces formally singular terms that have been difficult to handle for astrophysical applications. I will present a numerical implementation that addresses this difficulty by adapting Nützi’s regular nonlinear formulation to stationary hyperboloidal scri-fixing. In this formalism, null infinity and the matching interface to an interior simulation are at fixed grid locations. I will demonstrate this method on a vacuum benchmark including nonlinear gravitational-wave memory balance, extraction of radiation from a ten-orbit binary-black-hole inspiral through merger and ringdown, and dynamical Cauchy-hyperboloidal matching for nonlinearly perturbed black holes. I will explain the geometric and numerical ingredients behind these results and discuss the remaining steps toward efficient simulations extending from strong-field dynamics to radiation at infinity.
