- #106
PeterDonis
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But such a "spacelike surface" would in fact not be one, because it would have a "hole" at each singularity it intersects (since singularities are not part of the manifold). A similar remark would be true of a "spacelike surface" in a spacetime with one black hole and one singularity, that cut through the cylinder (the hole) "above" the point where the collapsing matter reaches the center (since that point is where the singularity begins). To make valid spacelike surfaces that do not have holes, you would need to "push" the central portion of the surface (the part inside each leg/cylinder) down below the point where the singularity begins (inside each leg/cylinder).PAllen said:This is what makes my intuition suggest a spacelike surface through all the legs before merger can, indeed, reach a singularity in each leg.
Once you've done that, it seems to me that there are no longer really two distinguishable alternatives: the "one singularity at the top of the trousers" case and the "multiple singularities branching down from the top of the trousers into each leg" case are actually the same, as far as anything inside the manifold is concerned.