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<p>We prove the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msubsup> <mi>C</mi> <mi mathvariant="normal">loc</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$C^{0,1}_{\mathrm{loc}}$</EquationSource> </InlineEquation>-inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msubsup> <mi>C</mi> <mi mathvariant="normal">loc</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$C^{0,1}_{\mathrm{loc}}$</EquationSource> </InlineEquation>-inextendibility from the blow-up of curvature. The assumed blow-up is expected to be satisfied for weak null singularities in the interior of generic rotating black holes. Thus, we expect the result presented here to directly contribute to the resolution of the <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msubsup> <mi>C</mi> <mi mathvariant="normal">loc</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$C^{0,1}_{\mathrm{loc}}$</EquationSource> </InlineEquation>-formulation of the strong cosmic censorship conjecture in a neighbourhood of subextremal Kerr.</p>

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Lipschitz inextendibility of weak null singularities from curvature blow-up

  • 期刊论文

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  • 发表日期：

    2025年11月11日

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  • Jan Sbierski

摘要

We prove the C loc 0 , 1 $C^{0,1}_{\mathrm{loc}}$ -inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer C loc 0 , 1 $C^{0,1}_{\mathrm{loc}}$ -inextendibility from the blow-up of curvature. The assumed blow-up is expected to be satisfied for weak null singularities in the interior of generic rotating black holes. Thus, we expect the result presented here to directly contribute to the resolution of the C loc 0 , 1 $C^{0,1}_{\mathrm{loc}}$ -formulation of the strong cosmic censorship conjecture in a neighbourhood of subextremal Kerr.