Comments on tails in Schwarzschild spacetimes

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.

Introduction expanded, references added, misprints corrected. To appear in CQG

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• The Huygens principle and cosmological gravitational waves in the Regge-Wheeler gauge
• Gravitational waves in Friedman-Lemaitre-Robertson-Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle
• Price's law for spin fields on a Schwarzschild background
• Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• Limit structure of Future Null Infinity tangent -topology of the event horizon and gravitational wave tail-