##GM / R^2## is not "the fall acceleration" except in a very technical sense: it is the "redshifted" proper acceleration of an observer "hovering" at ##R##. So, for example, if an observer at infinity were holding up an object at ##R## using a very long rope, ##GM / R^2## is the force per unit mass that the observer at infinity would have to exert on the rope. But the object at ##R## would not experience that acceleration; the object's proper acceleration would be ##GM / (R^2 \sqrt{1 - 2GM / (c^2 R)})##.Kekkuli said:
No, it isn't. You wouldn't notice anything special falling through the horizon because spacetime is locally Lorentzian there just like it is everywhere else. It has nothing to do with "fall acceleration".Kekkuli said:
Saying "notice" you seem to think of tidal force or spaghettification. Yes, the larger the black hole the less you feel it, as already said in #4. The reason is tidal force goes with 1/M².Kekkuli said:
Falling into a massive black hole without noticing means that an observer crossing the event horizon of a sufficiently large black hole would not experience any drastic changes or extreme tidal forces at that moment. The event horizon is the point beyond which nothing can escape the black hole's gravitational pull, but for very large black holes, this boundary can be crossed without any immediate dramatic effects.
In the case of a supermassive black hole, the event horizon is so large that the tidal forces at the boundary are relatively weak. This means that the difference in gravitational pull between your head and your feet (if you were falling feet first) is small, so you wouldn't feel significant stretching or squeezing forces, making the crossing unnoticeable.
Tidal forces are the differential gravitational forces experienced by an object in a gravitational field. Near a black hole, these forces can become extreme, stretching objects along the direction of the gravitational pull and compressing them perpendicularly. In smaller black holes, these forces are strong enough at the event horizon to be noticeable and potentially lethal. However, for supermassive black holes, these forces are much weaker at the event horizon, making them less noticeable.
Surviving the fall into a black hole is theoretically possible if the black hole is supermassive and the tidal forces are weak at the event horizon. However, once inside the event horizon, all paths lead inevitably to the singularity at the center, where the gravitational forces become infinitely strong, and survival is impossible. Additionally, the journey beyond the event horizon is one-way; escape is not possible.
After crossing the event horizon, you would continue to be pulled towards the black hole's singularity. The gravitational pull would become increasingly intense, and eventually, the tidal forces would become strong enough to overcome any structural integrity, leading to spaghettification, where you would be stretched and compressed. The exact experience of this process is not fully understood due to the extreme conditions and the limitations of our current physical theories.