论文标题
关于渐近电荷之间的关系，剥离的失败和延迟尾巴
On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails
论文作者
论文摘要
在过去的几年中，关于动力学，天体物理空间中重力辐射的渐近结构的数学进步很大。在本文中，我们从最近的作品中阐明了一些关键思想，并以新的方式组装它们，以使它们更容易成为更广泛的一般相对性社区。我们还在此过程中宣布了一些新的物理发现。 First, we introduce the conserved $f(r)$-modified Newman--Penrose charges on asymptotically flat spacetimes, and we show that these charges provide a dictionary that relates asymptotics of massless, general spin fields in different regions: Asymptotic behaviour near $i^+$ ("late-time tails") can be read off from asymptotic behaviour towards $\mathcal I^+$, and, similarly,可以从$ i^ - $或$ \ MATHCAL I^ - $的渐近行为中读取$ \ Mathcal I^+$的渐近行为。 然后，我们将使用此词典解释：（i）$ n $输液群体的四极近似值，从$ i^ - $ $ i^ - $导致“剥离属性到$ \ mathcal i^+$”，以及（ii）（ii）剥离偏离结果的失败与在晚期的惯常范围中的偏向范围的偏离预测，而宽度为宽度的范围，而不是格雷夫的范围，而不是散发出的范围，而不是格雷特（Graver）的范围，而不是等级的范围。 $rψ^{[4]} | _ {\ Mathcal I^+} \ sim u^{ - 6} $ as $ u \ to \ infty $，我们预测，$ r C^{[4]} | _ {\ Mathcal I^+} \ sim u^sim U^{ - sim U^{ - 3} $，与此latter a latter Ace ratter Ace ratter Ace ratter coefer cofer coefer cofe decear”无限过去的物质分布的时刻。
The last few years have seen considerable mathematical progress concerning the asymptotic structure of gravitational radiation in dynamical, astrophysical spacetimes. In this paper, we distil some of the key ideas from recent works and assemble them in a new way in order to make them more accessible to the wider general relativity community. We also announce some new physical findings in this process. First, we introduce the conserved $f(r)$-modified Newman--Penrose charges on asymptotically flat spacetimes, and we show that these charges provide a dictionary that relates asymptotics of massless, general spin fields in different regions: Asymptotic behaviour near $i^+$ ("late-time tails") can be read off from asymptotic behaviour towards $\mathcal I^+$, and, similarly, asymptotic behaviour towards $\mathcal I^+$ can be read off from asymptotic behaviour near $i^-$ or $\mathcal I^-$. Using this dictionary, we then explain how: (I) the quadrupole approximation for a system of $N$ infalling masses from $i^-$ causes the "peeling property towards $\mathcal I^+$" to be violated, and (II) this failure of peeling results in deviations from the usual predictions for tails in the late-time behaviour of gravitational radiation: Instead of the Price's law rate $rΨ^{[4]}|_{\mathcal I^+}\sim u^{-6}$ as $u\to\infty$, we predict that $rΨ^{[4]}|_{\mathcal I^+}\sim u^{-3}$, with the coefficient of this latter decay rate being a multiple of the monopole and quadrupole moments of the matter distribution in the infinite past.
