Towards Hyperboloidal Numerical Relativity with the Einstein Toolkit

The goal of hyperboloidal numerical relativity is to evolve the Einstein Field

Equations on compactified hyperboloidal slices, which are spacelike everywhere

and extend smoothly to future null infinity. This is the location in asymptotically flat

spacetimes reached by outgoing null rays, and where waveforms become fully

resolved. Including future null infinity in a finite computational domain is ideal for

gravitational wave extraction, which is typically done via extrapolation of Cauchy-

Characteristic extraction.

However, these methods introduce numerical inaccuracies

on the extracted waveforms and are not, in principal, a solution to the problem. In

this work, we evolve simple toy models of general relativity on background

spacetimes using compactified hyperboloidal slices. For this purpose, we use the

Einstein Toolkit, an extensive open-source program designed to support numerical

relativity simulations. We solve the toy models in first order in time and space and

find good convergence.

This work marks the first successful implementation of

hyperboloidal slicing within the Einstein Toolkit. It is a foundational step for future

development of these methods on the toolkit, and demonstrates its potential for

applications in numerical relativity.