A hyperboloidal study of tail decay rates for scalar and Yang-Mills fields

TL;DR

This paper examines how scalar and Yang-Mills fields decay over time near black holes, emphasizing the importance of null infinity for understanding gravitational wave signals and demonstrating effective numerical simulation methods.

Contribution

It introduces a hyperboloidal approach to study tail decay rates of fields on Schwarzschild backgrounds, enhancing the simulation of radiation signals in black hole spacetimes.

Findings

Null infinity is crucial for predicting gravitational wave signals.

Hyperboloidal methods improve numerical simulations of fields near black holes.

Decay rates of scalar and Yang-Mills fields are characterized on Schwarzschild backgrounds.

Abstract

We investigate the asymptotic behavior of spherically symmetric solutions to scalar wave and Yang-Mills equations on a Schwarzschild background. The studies demonstrate the astrophysical relevance of null infinity in predicting radiation signals for gravitational wave detectors and show how test fields on unbounded domains in black hole spacetimes can be simulated conveniently by numerically solving hyperboloidal initial value problems.