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Comment by idiotsecant

1 day ago

This is not true. There are some special exceptions (rotating kerr ring singularities) but in general there is no 'upward' direction away from the singularity. Space becomes timelike. There is only forward, toward the singularity. You can expend energy and accelerate toward the singularity slower, but every particle within the event horizon can move only closer to the singularity. There is absolutely no moving away from the singularity. Full stop. If you think there is, you are misunderstanding something fundamental about the model.

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idiotsecant

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raattgift  10 hours ago

> Space becomes timelike. There is only forward ...

No. It's a fanciful analogy on a particular family of coordinate charts, particuarly systems of coordinates which do not smoothly/regularly cross the horizon. The black hole interior is still part of a Lorentzian manifold, there is no change of the SO+(1,3) proper orthochronous Lorentz group symmetry at every point (other than spacetime points on the singularity). One can certainly draw worldlines on a variety of coordinate charts and add light-cones to them, and observe that the cones interior to the horizon all have their null surfaces intercept the singularity. However, there's lots of volume inside the interior light cones (and on the null surfaces) and nothing really constrains an arbitrary infaller's worldline, especially a timelike infaller, to a Schwarzschild-chart radial line (just as nothing requires arbitrary infallers to be confined to geodesic motion).

The interior segment of a Schwarzschild worldline in general can't backtrack in the r direction, but there are of course an infinity of elliptical trajectories which don't. (That is to say that all orbits across the horizon are plunging orbits; but one can also say that of large families of orbits that cross ISCO, which is outside the horizon).

A black hole with horizon angular momentum and general charges offer up different possibilities, as does the presence of any matter near (including interior to) the horizon (all of these also split the ISCO radius, move the apparent horizon, and may split the apparent and event horizons). The Schwarzschild solution of course is a non-spinning, chargeless, vacuum solution everywhere, and is maximally symmetrical, and is usually probed with a test particle. An astrophysical system like a magnetic black hole formed that passes through a jet from a companion pulsar, for example, does not neatly admit the Schwarzschild chart (and has no known exact analytical solution to the field equations). At least one such astrophysical binary is known (in NGC 1851 from TRAPUM/MeerKAT) (and if you don't immediately run away from A. Loeb papers like you should, he added his name to one that argues there are thousands of such systems in the galaxy centre near Sgr A*, which itself is now known to have strong magnetic fields (thanks to EHT's study of the polarized ring)).