It's not quite true that everything feels normal. If I am standing with my feet toward the singularity, my hand cannot move above my head, the best it can do is fall toward the singularity slower than my head does. Especially at very slow speeds this has some very weird physical effects, not the least of which is the immediate impossibility of all systems that make you 'you' continuing to function.
Is this true?
My understanding is that for extremely large black holes the tidal forces are negligible near the event horizon. So things should function pretty much the same other than you can't move in reverse and get out.
If two rockets fall past the horizon at the same time, one accelerating forward towards the singularity, and the other accelerating backwards away from the singularity, then shouldn't the distance between the rockets increase, even though they are both moving inexorably forward?
If the tidal forces are low, I'd assume that my muscles are still strong enough to "slow down my hand enough" to move it above my head.
The relevant quantities are the curvature scalars near the horizon, and for a sizable black hole they are small there. As an example, consider the Kretschmann scalar (KS). The KS is the sum of the squares of all components of a tensor. In Schwarzschild spacetime KS looks like R_{\mu\nu\lambda\rho}R^{\mu\nu\lambda\rho} = (48 G^2M^2)/(c^4r^6), where R is the Riemann curvature tensor, and we can safely set G=1 and c=1 so (48 M^2)/r^6. In this setting, KS is proportional to the spacetime curvature. At r = 2M, the Schwarzschild radius, the number becomes very small as we increase M, the black hole's mass. However, for any M at r = 0, the Kretschmann scalar diverges.
For a large-M black hole, there is "no drama" for a free-faller crossing the event horizon, as the KS gradient is tiny.
Since the crosser is in "no drama" free-fall he can raise his hands, toss a ball between his hands, throw things upwards above his head, and so forth. The important thing though is that all these motions are most easily thought of in his own local self-centred freely-falling frame of reference, and not against the global Schwarzschild coordinates. His local frame of coordinates is inexorably falling inwards. Objects moving outwards in his local frame are still moving inwards against the Schwarzschild coordinates.
You might compare with a non-freely-falling frame of reference. Your local East-North-Up (ENU) coordinates let you throw things upwards or eastwards, but in less-local coordinates your ENU frame of reference is on a spinning planet in free-fall through the solar system (and the solar system is in free-fall through the Milky Way, and the galaxy is in free-fall through the local group). That your local ENU is not a freely-falling set of coordinates does not change that the planet is in free-fall, and your local patch of coordinates is along for the ride.
A comparison here would be a long-running rocket engine imparting a ~ 10 m s^-1 acceleration to a plate you stand on. In space far from the black hole, you and the rocket engine would tend to move away from the black hole, but you'd be able to do things like juggle or jump up and down, and it'd feel like doing it on Earth's surface. This is a manifestation of the equivalence principle. Inside the horizon the rocket would still be accelerating the plate and you at ~ 10 m s^-1, but you, the plate, and the rocket would all be falling inwards.
Tidal forces are not the constraining factor - the transformation of space into a timeline property is. There is no out, no away direction. All paths lead to singularity. No particle can travel away from singularity .
Two rockets can diverge in distance, because one is slowing itself along the timeline space dimension toward singularity. If you are moving 1 m/s toward singularity, the fastest your hand can raise above your head is 1 m/s with infinite energy expenditure. The same goes for blood pumping to your head, electrical impulses to your brain, etc.
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.
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.
> 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)).
You really laid the text on thick here to end up exactly conceding the point.
That doesn't sound right. If you're on the event horizon you're not going at very slow speeds in that sense, the space around you is already falling into the black hole faster than light.
If you're "travelling at 1m/s so you can only raise your hand above your head at 1m/s by expending infinite energy" then you're already travelling at c-1m/s away from the black hole through local space just to 'stay still' at 1m/s 'velocity'. No wonder you need infinite energy to accelerate your arm 1m/s further and things get weird - you're travelling at relativistic velocities.
nor can you swivel your head to look backwards, as all the particles in your head are tidal locked in a falling trajectory towards the center