<p>Using a purely physical-space analysis, we prove the precise oscillatory blow-up asymptotics of the spin <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5332_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(+2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> Teukolsky field in the interior of a subextremal Kerr black hole. In particular, this work gives a new proof of the blueshift instability of the Kerr Cauchy horizon against linearized gravitational perturbations that was first shown by Sbierski (Ann PDE 9:Art. 7, 2023). In that sense, this work supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. The proof is an extension to the Teukolsky equation of the work by Ma and Zhang (Trans Am Math Soc 376:7815–7856, 2023) that treats the scalar wave equation in the interior of Kerr. The analysis relies on the generic polynomial decay on the event horizon of solutions of the Teukolsky equation that arise from compactly supported initial data, as recently proved by Ma and Zhang (Comm Math Phys 401:433–434, 2023) and Millet (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5332_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\(|{\textrm{a}}| &lt; \text {M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mtext>a</mtext> <mo stretchy="false">|</mo> <mo>&lt;</mo> <mtext>M</mtext> </mrow> </math></EquationSource> </InlineEquation>, 2023, <a href="http://arxiv.org/abs/2302.06946">arXiv:2302.06946</a>) in subextremal Kerr.</p>

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Precise Asymptotics of the Spin +2 Teukolsky Field in the Kerr Black Hole Interior

  • Sebastian Gurriaran

摘要

Using a purely physical-space analysis, we prove the precise oscillatory blow-up asymptotics of the spin \(+2\) + 2 Teukolsky field in the interior of a subextremal Kerr black hole. In particular, this work gives a new proof of the blueshift instability of the Kerr Cauchy horizon against linearized gravitational perturbations that was first shown by Sbierski (Ann PDE 9:Art. 7, 2023). In that sense, this work supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. The proof is an extension to the Teukolsky equation of the work by Ma and Zhang (Trans Am Math Soc 376:7815–7856, 2023) that treats the scalar wave equation in the interior of Kerr. The analysis relies on the generic polynomial decay on the event horizon of solutions of the Teukolsky equation that arise from compactly supported initial data, as recently proved by Ma and Zhang (Comm Math Phys 401:433–434, 2023) and Millet ( \(|{\textrm{a}}| < \text {M}\) | a | < M , 2023, arXiv:2302.06946) in subextremal Kerr.