4 ms·
For a sufficiently large black hole tidal effects are weak near the horizon, but inwards from there the Weyl tensor (or the contraction to an appropriate curvat
by raattgift 3y ago
For a sufficiently large black hole tidal effects are weak near the horizon, but inwards from there the Weyl tensor (or the contraction to an appropriate curvature scalar; the Weyl tensor itself is a contraction of the Riemann curvature tensor essentially encoding body-deforming curvature which preserves the body's volume) grows to the point where there will be inevitable failure under the stretch-squash. Indeed the Kretschmann curvature scalar eventually diverges, and that fact is what indicates the presence of a singularity.
Roughly, the available paths for elements of a spherical cloud of noninteracting dust will tend to deform the sphere into a prolate ellipsoid like an American football, with the long axis aligned radially, i.e., with one end pointing to the strong curvature inside the black hole. The dust's overall volume is preserved, so there must be a squashing along the other two spatial axes. As infall proceeds, the prolation extremizes -- in due course the cloud resembles a piece of string with a slight bulge along its length.
A round football has internal interactions which try to keep it round, and so is different from a sphere or shell of non-interacting dust. However, it will still be stretch-squashed as it infalls and gravitation tries to make it look like an American football. Soon enough it will tear and burst. A human in free fall will probably end up firstly rotated feet-first or head first, and quickly will feel some discomfort from the stretch-squashing, eventual disarticulation of joints, tearing of the skin and other tissues, and so on. While it still works, the human's wristwatch will count of on the order of minutes between its crossing of the large black hole's horizon and its mechanical failure.
For stellar ("little") black holes, the Weyl tensor is large enough to cause this sort of bursting (and wristwatch failure) outside the horizon.