Peeling-off behaviour of the wave equation on the Vaidya spacetime

TL;DR

This paper investigates the peeling behaviour of solutions to the wave equation on Vaidya spacetime, establishing optimal initial data classes for regularity at null infinity using energy and conformal techniques.

Contribution

It extends the peeling analysis to Vaidya spacetime, identifying initial data classes ensuring regularity comparable to Minkowski and Schwarzschild cases.

Findings

Identifies optimal initial data classes for regularity at null infinity.

Shows equivalence of data classes with Minkowski and Schwarzschild spacetimes.

Combines conformal and energy methods for analysis.

Abstract

We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason-Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterised by Sobolev-type norms, in terms of corresponding function spaces of initial data. All function spaces are obtained from energy fluxes associated with an observer constructed from the Morawetz vector field on Minkowski spacetime. We combine conformal techniques and energy estimates to obtain the optimal classes of initial data ensuring a given regularity of the rescaled field. The classes of data are equivalent with those obtained on Minkowski and Schwarzschild spacetimes in that they impose the same decay at infinity and regularity.