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arXiv:2205.14808math.AP

Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes

Elena Giorgi, Sergiu Klainerman, Jeremie Szeftel

Abstract

This is the last part of our proof of the nonlinear stability of the Kerr family for small angular momentum, i.e $|a|/m\ll 1$, in which we deal with the nonlinear wave type estimates needed to complete the project. More precisely we provide complete proofs for Theorems M1 and M2 as well the curvature estimates of Theorem M8, which were stated without proof in sections 3.7.1 and 9.4.7 of \cite{KS:Kerr}. Our procedure is based on a new general interest formalism (detailed in Part I of this work), which extends the one used in the stability of Minkowski space. Together with \cite{KS:Kerr} and the GCM papers \cite{KS-GCM1}, \cite{KS-GCM2}, \cite{Shen}, this work completes proof of the Main Theorem stated in Section 3.4 of \cite{KS:Kerr}.

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math.APAnalysis of PDEs

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  1. In a major discovery, scientists say space-time churns like a choppy sea 1 comment

    • That's an unexpectedly neat question. Gravitational radiation can form caustics, so in one way, yes. This was an area of theory that Bondi and Pirani were interested in during the 60s to 80s. Caustics are meant in the sense of the bright spots in…

      raattgiftView on HNParent context

  2. Black holes finally proven mathematically stable 4 comments

    • check for yourself: https://arxiv.org/pdf/2205.14808.pdf

      untiltedView on HNParent context

    • Pdfs are readable by machines. It's also released as tex. https://arxiv.org/format/2205.14808 Huh. this account apparently got shadowbanned. Guess it's another good reminder not to post here.

      archgoonView on HNParent context

    • Almost all arXiv submitters (and certainly any serious one in a category like this paper's math.AP (Mathematics / Analysis of Partial Differential Equations) <https://arxiv.org/list/math.AP/new>; click the "other" in "[pdf, ps, other]" and there click Download sources) will…

      raattgiftView on HNParent context

    • tl;dr: gravitational waves do hard-to-calculate things inside a strong ergoregion around a fast-spinning black hole, and may do hard-to-calculate things to the black hole, and those calculations are outside the scope of the paper. > [how to define] 'slowly rotating' [might be]…

      raattgiftView on HNParent context

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