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    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that An isometry between neighborhoods of spacelike hypersurfaces in two vacuum solutions is not in general extendible to an isometry between their future domains of dependence.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The surgical removal of points from a vacuum solution exploits the non-uniqueness of maximal extensions, not indeterminism in the physics itself.
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      Think about whether this reason is strong or weak

    • 2.Earman and Norton's hole argument shows such underdetermination reflects representational redundancy in diffeomorphism-invariant theories, not genuine physical ambiguity.
      ?

      Think about whether this reason is strong or weak

    • 3.A physically meaningful notion of determinism should be formulated over equivalence classes of diffeomorphically related models, rendering the non-extendibility result physically vacuous.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The counterexample relies on solutions that are not globally hyperbolic, but Penrose and Hawking's singularity theorems suggest physically realistic spacetimes satisfy strong causality conditions.
      ?

      Think about whether this reason is strong or weak

    • 2.Restricting the domain of GR to globally hyperbolic spacetimes, as advocated by Geroch's development theorem, restores a robust form of Laplacian determinism within that class.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Starting from any vacuum solution, one can remove a closed set of points lying to the future of a neighborhood of a spacelike hypersurface and within its future domain of dependence.
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      Think about whether this reason is strong or weak

    • 2.The surgically altered manifold with the restricted metric is also a solution to the vacuum Einstein equations.
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    • 3.The original and surgically altered solutions share isometric neighborhoods but their future domains of dependence are not isometric.
      ?

      Think about whether this reason is strong or weak

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