Peeling for tensorial wave equations on Schwarzschild spacetime

TL;DR

This paper proves the peeling property for tensorial wave equations on Schwarzschild spacetime, demonstrating optimal decay and asymptotic behavior of solutions near null infinity using conformal and vector field methods.

Contribution

It introduces a novel combination of conformal compactification and vector field techniques to establish peeling for tensorial fields on Schwarzschild spacetime.

Findings

Established peeling property for tensorial Fackrell-Ipser and spin ±1 Teukolsky equations.

Proved two-sided energy estimates at null infinity and initial hypersurface.

Achieved optimal initial data conditions for peeling at all orders.

Abstract

In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $\pm 1$ 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 $\mathscr{I}^\pm$ and the initial Cauchy hypersurface $\Sigma_0 = \left\{ t=0 \right\}$ in a neighbourhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.