Comments on tails in Schwarzschild spacetimes

TL;DR

This paper provides a detailed numerical study of late-time wave decay in Schwarzschild spacetime, confirming specific power-law falloff behaviors for different wave types and initial conditions.

Contribution

It offers new numerical evidence for the decay rates of scalar, electromagnetic, and gravitational waves in Schwarzschild spacetime, clarifying their late-time tail behavior.

Findings

Scalar monopole waves decay as 1/t^{2l+3}

Electromagnetic dipole waves decay as 1/t^{2l+3}

Gravitational axial quadrupole waves decay as 1/t^{2l+3}

Abstract

We performed a careful numerical analysis of the late tail behaviour of waves propagating in the Schwarzschild spacetime. Specifically the scalar monopole, the electromagnetic dipole and the gravitational axial quadrupole waves have been investigated. The obtained results agree with a falloff $1/t^{2l+3}$ for the general initial data and $1/t^{2l+4}$ for the initially static data.