And it would take 10 days from event horizon to the singularity.
https://modern-physics.org/time-dilation-near-massive-bodies...
This is the origin of my favorite science fiction theory. (little to no actual science but you could write a fun space romp around it) If you get a large enough black hole where the tidal forces will not rip you to shreds instantly, you could just scoot across the event horizon right, now what happens? you can still move around, everything feels normal, but really you have lost half a dimension, everything "out" from the center is completely gone from the universe. Now the theory, back to our universe, What happened to time? why does time only go one way? we can accelerate and decelerate along the time axis, but can't reverse it. Where has our missing half of a time dimension gone?
Wouldn't that just mean that the singularity is located infinitely far into the future?
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.
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.
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.
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)).
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".
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.
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.
It takes infinite time to reach event horizon, not the center.
But in this specific case, you get one odd conclusion. if it takes forever to enter a black hole. is it impossible for anything to pass the event horizon? It sounds like this is observation dependent. but from an external point of view you are unable to observe anything entering the black hole. and from an internal point of view, the universe will instantly age and die when you try and enter the hole.(and if hawking radiation actually exists you will see the black hole shrink and pop the instant you try and enter it) either way nothing is getting in.
Is most of the mass of the star that formed the black hole actually stuck in a time dilated shell just outside the event horizon? Or perhaps all the mass is eternally stuck collapsing. and never actually reaches the density required to pass the event horizon. is that another way to define the event horizon? the point where time stops.
Time dilation makes my head hurt.
Even that is only true to a distant observer, not the one crossing the horizon.
The outside observer’s view doesn’t stop physics inside. For a massive black hole, you absolutely do reach the singularity in finite time by your own clock.. likely minutes to hours for the largest ones we've known about so far.
Your “sightseeing tour” would be a kaleidoscope of light as it brushes past you on its way to the singularity.
Eventually your atoms will make their way to the center singularity.
in a black hole time and space get switched in a sense.