Peeling for tensorial wave equations on Schwarzschild spacetime

Abstract

In this paper, we establish the asymptotic behavior along outgoing and incoming radial geodesics, i.e. the peeling property for the tensorial Fackerell–Ipser and spin [Formula: see text] Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity [Formula: see text] and the initial Cauchy hypersurface [Formula: see text] in a neighborhood of spacelike infinity [Formula: see text] far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.