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• W4287180824 abstract "In this paper, we expand on results from our previous paper The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples [1] by showing that the failure of peeling (and, thus, of smooth null infinity) in a neighbourhood of $i^0$ derived therein translates into logarithmic corrections at leading order to the well-known Price's law asymptotics near $i^+$. This suggests that the non-smoothness of $mathcal{I}^+$ is physically measurable. More precisely, we consider the linear wave equation $Box_g phi=0$ on a fixed Schwarzschild background ($M>0$), and we show the following: If one imposes conformally smooth initial data on an ingoing null hypersurface (extending to $mathcal{H}^+$ and terminating at $mathcal{I}^-$) and vanishing data on $mathcal{I}^-$ (this is the no incoming radiation condition), then the precise leading-order asymptotics of the solution $phi$ are given by $rphi|_{mathcal{I}^+}=C u^{-2}log u+mathcal{O}(u^{-2})$ along future null infinity, $phi|_{r=R>2M}=2Ctau^{-3}logtau+mathcal{O}(tau^{-3})$ along hypersurfaces of constant $r$, and $phi|_{mathcal{H}^+}=2Cv^{-3}log v+mathcal{O}(v^{-3})$ along the event horizon. Moreover, the constant $C$ is given by $C=4M I_0^{(mathrm{past})}[phi]$, where $I_0^{(mathrm{past})}[phi]:=lim_{uto -infty} r^2partial_u(rphi_{ell=0})$ is the past Newman--Penrose constant of $phi$ on $mathcal{I}^-$. Thus, the precise late-time asymptotics of $phi$ are completely determined by the early-time behaviour of the spherically symmetric part of $phi$ near $mathcal{I}^-$. Similar results are obtained for polynomially decaying timelike boundary data. The paper uses methods developed by Angelopoulos--Aretakis--Gajic and is essentially self-contained." @default.
• W4287180824 created "2022-07-25" @default.
• W4287180824 creator A5013707666 @default.
• W4287180824 date "2021-05-17" @default.
• W4287180824 modified "2023-10-14" @default.
• W4287180824 title "The Case Against Smooth Null Infinity II: A Logarithmically Modified Price's Law" @default.
• W4287180824 doi "https://doi.org/10.48550/arxiv.2105.08084" @default.
• W4287180824 hasPublicationYear "2021" @default.
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