Corpus ID: 235265801

The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $\ell$-Modes of Linear Waves on a Schwarzschild Background

@inproceedings{Kehrberger2021TheCA,
  title={The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher \$\ell\$-Modes of Linear Waves on a Schwarzschild Background},
  author={Leonhard M. A. Kehrberger},
  year={2021}
}
In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on $\mathcal I^-$ and polynomially decaying data, $r\phi_\ell\sim t^{-1}$ as $t\to-\infty$, on either a timelike boundary of constant area radius (I) or an ingoing null hypersurface (II). In case (I), we show that the asymptotic expansion of $\partial_v(r\phi_\ell… Expand

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