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OpenAI reports generic weak future inextendibility near rotating Kerr

Individual problem

For each fixed subextremal rotating Kerr bridge (M > 0 and 0 < |a| < M), smooth vacuum data in a sufficiently small weighted tenth-order neighborhood whose full maximal globally hyperbolic development admits a future continuous, nondegenerate Lorentzian extension with locally square-integrable weak connection form a meagre set.

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OpenAI reports generic weak future inextendibility near rotating Kerr

  • Mathematics
  • Theoretical Physics

For each fixed subextremal rotating Kerr bridge (M > 0 and 0 < |a| < M), smooth vacuum data in a sufficiently small weighted tenth-order neighborhood whose full maximal globally hyperbolic development admits a future continuous, nondegenerate Lorentzian extension with locally square-integrable weak connection form a meagre set. Hence inextendible data are residual in the weighted smooth topology.

AI involvementAI-led
ImportanceMajor
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

For each fixed subextremal rotating Kerr bridge (M > 0 and 0 < |a| < M), smooth vacuum data in a sufficiently small weighted tenth-order neighborhood whose full maximal globally hyperbolic development admits a future continuous, nondegenerate Lorentzian extension with locally square-integrable weak connection form a meagre set. Hence inextendible data are residual in the weighted smooth topology.

Why it matters

If correct, gives a generic near-Kerr strong cosmic censorship result at the square-integrable-connection threshold for the entire future development.

What counts as progress

Are future C⁰ ∩ W¹,² extensions nongeneric for smooth vacuum data near a fixed rotating Kerr bridge?

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