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The Case Against Smooth Null Infinity V: Early-Time Asymptotics of Linearised Gravity Around Schwarzschild for Fixed Spherical Harmonic Modes by Kehrberger, Leonhard; Masaood, Hamed is a scholarly article available to read on EtoBox.

What is The Case Against Smooth Null Infinity V: Early-Time Asymptotics of Linearised Gravity Around Schwarzschild for Fixed Spherical Harmonic Modes about?

Starting from Post-Newtonian predictions for a system of $N$ infalling masses from the infinite past, we formulate and solve a scattering problem for the system of linearised gravity around Schwarzschild as introduced in [DHR19]. The scattering data are posed on a null hypersurface $\mathcal C$ emanating from a section of past null infinity $\mathcal I^-$, and on the part of $\mathcal I^-$ that lies to the future of this section: Along $\mathcal C$, we implement the Post-Newtonian theory-inspired hypothesis that the gauge-invariant components of the Weyl tensor $\alpha$ and $\underline{\alpha}$ (a.k.a. $\Psi_0$ and $\Psi_4$) decay like $r^{-3}$, $r^{-4}$, respectively, and we exclude incoming radiation from $\mathcal I^-$ by demanding the News function to vanish along $\mathcal I^-$. We also show that compactly supported gravitational perturbations along $\mathcal I^-$ induce very similar data, with $\alpha$, $\underline{\alpha}$ decaying like $r^{-3}$, $r^{-5}$ along $\mathcal C$. After constructing the unique solution to this scattering problem, we provide a complete analysis of the asymptotic behaviour of projections onto fixed spherical harmonic number $\ell$ near spacelike $i^

Author

Kehrberger, Leonhard; Masaood, Hamed

Published

2024

Language

EN