[snowwrestler]

You can move away from a singularity once you are inside the event horizon. You just can’t achieve escape velocity anymore once you’re inside the event horizon.

After you pass the event horizon, all your possible paths become elliptical. That doesn’t mean all possible paths instantly point directly at the center.

[idiotsecant]

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.

[raattgift]

> 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)).

[idiotsecant]

You really laid the text on thick here to end up exactly conceding the point.

[raattgift]

No, not really. To boil it down to thinner text, and to focus on your "Space becomes timelike", I think you are stuck on (a) a particular system of coordinates that (b) are not regular across the horizon and (c) thinking that either of these does anything physical to free-falling infalling test particle.

The huge flashing red warning sign on (a) & (c) is that you drop in the words "'upward' direction", "{toward, closer to, away from} the singularity" and most especially "slower": you are clearly implicitly slicing spacetime into space and time.

If you can handle thicker text, Unruh has a nice discussion of regular systems of coordinates at http://theory.physics.ubc.ca/530-21/bh-coords2.pdf Additionally, Martel & Poisson 2001 <https://pubs.aip.org/aapt/ajp/article-abstract/69/4/476/1055...> (arXiv version <https://arxiv.org/abs/gr-qc/0001069>) is a nice discussion of PG coordinates.

More visually, one can compare the light cone structure on a KS diagram like at <https://tikz.net/relativity_kruskal_diagram/> (just before the "Edit and compile if you like") and a randomly chosen but very typical diagram in Schwarzschild coordinates <https://www.researchgate.net/profile/Ward-Vleeshouwers/publi...> or (in German) <https://yukterez.net/f/einstein.equations/files/schwarzschil...> (hovering over a diagram displays some light cones). Which cone appears to topple over in their respective coordinate charts is pretty obvious, and should give you plenty of shaded grey to think about the coordinate-dependence of "Space becomes timelike".