Spacelike matching to null infinity

TL;DR

This paper introduces two methods to include null infinity in numerical simulations of spacetime, enabling accurate radiation extraction and boundary treatment, demonstrated on scalar fields in Kerr spacetime.

Contribution

It presents geometric and coordinate-based methods to incorporate null infinity into numerical codes with minimal modifications, enhancing simulation accuracy.

Findings

Successfully applied methods to Kerr spacetime

Confirmed tail decay rates at null infinity

Enhanced simulation of radiative zones

Abstract

We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The first method is based on the geometric conformal approach, the second is a coordinate based approach. We apply these methods to the case of a massless scalar wave equation on a Kerr spacetime. Our methods are designed to allow existing codes to reach the radiative zone by including future null infinity in the computational domain with minor modifications. We demonstrate the flexibility of the methods by considering both Boyer-Lindquist and ingoing Kerr coordinates near the black hole. We also confirm numerically predictions concerning tail decay rates for scalar fields at null infinity in Kerr spacetime due to Hod for the first time.