This thread is a sidetrack from zanket's thread: (Alpha) General relativity is self-inconsistent v3 - Pete

zanket,
The OP does not say that the rod was gravitationally accelerating toward the horizon. The only information given about the rod’s motion is that the part of it that is above the horizon is escaping to r=infinity.
Seems James R already addressed this point. Your OP stated "Let a freely falling rod span the horizon of a black hole..." Yes, a 'freely falling rod' is gravitationally accelerating toward the event horizon whether you use those exact words or not, explained earlier. Next, you state "Let the part of the rod above the horizon be excaping to r=infinity". That part of the rod is accelerating in the opposite direction as the 'freely falling' lower part.
Not all of the supporting info in the other thread applies to this thread. The thought experiment in this thread does not rely on SR.
Of course the thought experiment in this thread relies on SR's flat spacetime inertial frames. Your whole gedanken is a challenge to Minkowski flat spacetime and Schwarzchild black holes. Those are both Special Theory formulations, not General Relativity's curved spacetime. GR's curved spacetime was what led to Kerr black holes, the ones we have observational evidence for in the universe. No evidence for Schwarzchild black holes has ever been found, meaning that no black holes have been found that are definitely not rotating. Of course, the properties of all black holes have not been measured to determine if they are rotating or not, just that the ones we were capabale of measuring have a flat accretion disk rotating at very near the speed of light at the event horizon. How could that rotation suddenly cease at the point immediately below the event horizon?

Your references to tidal forces are both based on Schwarzchild formulations which predict a central singularity. They are assuming tidal forces decrease in intensity at an inverse cube ratio radially from that point singularity. Again, that is SR mathematics, not GR's curved spacetime. There is no point singularity in GR's Kerr black holes, but a ring-shaped singularity that lies inside the event horizon. Tidal forces in Kerr black holes are immense near the event horizon because of the proximity of the ring singularity to the event horizon. Tidal forces, however, can be weak in the center of a very large Kerr black hole, a GR black hole.

Your OP stated "Let a freely falling rod span the horizon of a black hole..." Yes, a 'freely falling rod' is gravitationally accelerating toward the event horizon whether you use those exact words or not, explained earlier.
No, a freely falling object need not be gravitationally accelerating toward the horizon. Why do you think otherwise? The definition of “freely falling” is given in the supporting info. Where do you see the definition say that the object has to be moving in a particular direction? When a ball is thrown up in the air, it is freely falling even as its altitude increases.

Of course the thought experiment in this thread relies on SR's flat spacetime inertial frames. Your whole gedanken is a challenge to Minkowski flat spacetime and Schwarzchild black holes.
It is not a challenge to Minkowski flat spacetime. The proof does not rely on SR. What statement in the proof do you think shows that the proof relies on SR?

No evidence for Schwarzchild black holes has ever been found, meaning that no black holes have been found that are definitely not rotating.
That doesn’t matter. The OP is about theory, not reality. Do you realize that a theory can be self-inconsistent regardless how its predictions match reality?

How could that rotation suddenly cease at the point immediately below the event horizon?
The question is irrelevant since the OP is about theory, not reality.

Your references to tidal forces are both based on Schwarzchild formulations which predict a central singularity. They are assuming tidal forces decrease in intensity at an inverse cube ratio radially from that point singularity. Again, that is SR mathematics, not GR's curved spacetime. ...
The OP says “Let a freely falling rod span the horizon of a black hole so large that the tidal force on the rod is negligible”. GR allows the tidal force to be negligible at a horizon, if only for a Schwarzschild black hole. I’ve given two references to support that. It doesn’t matter whether Schwarzschild black holes occur in reality, because the OP is about theory, not reality. The supporting info notes that tidal force is synonymous with spacetime curvature. Then tidal forces are predicted by GR, not SR. You have not identified a problem with the OP in your paragraph.

zanket,
No, a freely falling object need not be gravitationally accelerating toward the horizon. Why do you think otherwise?
Because that is the very definition of a freely falling reference frame in your gedanken. In a freely falling reference frame, gravity is the only force present and a particle accelerates toward the source of the gravity. An opposing force is required to alter this acceleration. The frame then becomes a non-inertial frame once this opposing force is evident. A freely falling frame cannot be 'falling' in any direction except directly toward the source of the gravitational acceleration, or it is not a freely falling frame. Also, SR inertial frames are Global reference frames, meaning one can extent the frame's coordinates through all of space and time. GR inertial frames only constitute are very small area and cannot be extended because curved spacetime will not allow a rigid system of clocks and rods to be set up. The bottom of your rod, even if it was just free falling toward the event horizon, would be in a different inertial frame than the top of the rod because of the intensely curved spacetime near an event horizon. The tidal forces could only be 'neglected' if the size of the inertial frame was very, very tiny.


Where do you see the definition say that the object has to be moving in a particular direction? When a ball is thrown up in the air, it is freely falling even as its altitude increases.
Your ball required an opposing force (non-inertial) to initially change the direction of the ball (up). You invalidated your gedanken with the ball observation. The ball will change direction and freely fall toward the gravitating body unless escape velocity is exceeded and maintained. Since escape velocity in your gedanken in near the speed of light, it would require a constant force to keep your 'rod' moving away from the event horizon, a non-inertial frame of reference.
It is not a challenge to Minkowski flat spacetime. The proof does not rely on SR. What statement in the proof do you think shows that the proof relies on SR?
Do you understand the difference between a 'free-float' inertial frame as used in Minkowski flat spacetime (SR) and a 'freely falling' inertial frame as used in Schwarzschild spacetime (GR)? You are using the properties of a Global SR-type 'free-float' reference frame in Schwarzschild time. The two frames are similar, but not identical. Differences are in their size, gravitational interaction, and tidal forces. A freely falling reference frame cannot 'float' away from a gravitating object, as you suggest in your OP.

zanket,

Because that is the very definition of a freely falling reference frame in your gedanken. In a freely falling reference frame, gravity is the only force present and a particle accelerates toward the source of the gravity.

"Accelerating toward" doesn't mean "moving toward".
A ball thrown into the air is in freefall on the way up as well as the way down.

Pete,
"Accelerating toward" doesn't mean "moving toward".
A ball thrown into the air is in freefall on the way up as well as the way down.
Yes it does. Your ball required an inertial force to momentarily change it course through spacetime. After the force is removed, the ball will continue its path toward the gravitating object.

When the ball is on the way up, it is not being acted on by any force except gravity. It is in freefall. It is accelerating toward Earth, and moving away from Earth.

When the ball is on the way up, it is not being acted on by any force except gravity. It is in freefall. It is accelerating toward Earth, and moving away from Earth.
The ball required an initial acceleration opposite, and greater, than the acceleration of gravity to begin to move 'up'. In a free float inertial frame, the ball will continue to move 'up' until another force is applied. That would be a flat spacetime inertial frame, where the ball continued to move at a constant speed. In curved spacetime, the ball will return to Earth. You tell me why it does so, Pete.

And why did you separate this thread? The understanding of why is essential to zanket's OP.

I separated the thread because it's an irrelevant sidetrack, adequately addressed in the posts I left behind.

In curved spacetime, the ball will return to Earth only if it is moving slower than escape velocity. If it isn't, it will continue to both move away from Earth an accelerate toward Earth indefinitely.