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    The point at the center of a Schwarzschild black hole arg... — Carmelics
    Home/Free Will & Foreknowledge
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    The point at the center of a Schwarzschild black hole arguably does not exist as part of space-time

    Free Will & Foreknowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Near the center of a Schwarzschild black hole, curvature increases without bound
      ?

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    • 2.At the center of a Schwarzschild black hole, curvature is undefined
      ?

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    • 3.Where curvature is undefined, Einstein's field equations cannot be said to hold
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Mathematical singularities can be treated as limit points or boundary constructions that preserve their membership in an extended space-time manifold.
      ?

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    • 2.Geroch, Kronheimer, and Penrose's 1972 c-boundary construction formally incorporates singular endpoints into space-time topology without requiring field equations to hold there.
      ?

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    • 3.The failure of a physical law at a point is insufficient to exclude that point from the underlying geometric structure the law presupposes.
      ?

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    Reason against 2 of 2
    ?
    • 1.The Schwarzschild solution is a coordinate-dependent idealization; no realistic collapsed star produces a perfect Schwarzschild geometry, so the 'center' is a model artifact, not a physical absence.
      ?

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    • 2.Eliminating entities from ontology solely because they produce divergences in a theory commits the instrumentalist fallacy of conflating theoretical breakdown with non-existence.
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    Related

    At the center of a Schwarzschild black hole, curvature is undefinedEliminating entities from ontology solely because they produce divergences in a ...Geroch, Kronheimer, and Penrose's 1972 c-boundary construction formally incorpor...Mathematical singularities can be treated as limit points or boundary constructi...
    +5 moreShow less
    Near the center of a Schwarzschild black hole, curvature increases without boundPoints where Einstein's equations do not hold arguably do not exist as parts of ...The Schwarzschild solution is a coordinate-dependent idealization; no realistic ...The failure of a physical law at a point is insufficient to exclude that point f...Where curvature is undefined, Einstein's field equations cannot be said to hold

    Similar

    At the center of a Schwarzschild black hole, curvature is undefined79%Near the center of a Schwarzschild black hole, curvature increases wit...74%Points where Einstein's equations do not hold arguably do not exist as...71%Separating space-time structures into manifold and metric opens up pro...64%

    Source

    AI-extracted1/3 agreementValid
    SEP: determinism-causal
    View source passageHide passage
    The separation of space-time structures into manifold and metric (or connection) facilitates mathematical clarity in many ways, but also opens up Pandora’s box when it comes to determinism. The indeterminism of the Earman and Norton hole argument is only the tip of the iceberg; singularities make up much of the rest of the berg. In general terms, a singularity can be thought of as a “place where things go bad” in one way or another in the space-time model. For example, near the center of a Schwa
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit