Tidal Forces When Falling into a Black Hole

[jartsa]

So, if the Earth moves slowly through a large hula hoop, sensors attached on the hoop will measure some stresses, which we might call tidal forces.

The faster the Earth moves relative to the hoop the larger those tidal forces are.

So, if a person falls into a black hole, there are some tidal forces, and the speed of the person relative to the black hole tends to become very large. Do tidal forces depend on speed in this case too?

I mean, those transverse tidal forces that try to compress the person seem to be the same type of tidal forces that the hula hoop felt.Here the effect of speed on force of gravity is discussed:
https://www.physicsforums.com/threa...er-if-they-run-over-a-scale-very-fast.957827/

 

[PeterDonis]

The faster the Earth moves relative to the hoop the larger those tidal forces are.

Why do you think this is the case?

the speed of the person relative to the black hole

What do you mean by this? This doesn't even look like a well-defined concept to me.

Here the effect of speed on force of gravity is discussed

That thread has nothing to do with tidal forces; the scenario being discussed in that thread is not the same as either of the ones you are proposing here.

 

[russ_watters]

So, if the Earth moves slowly through a large hula hoop, sensors attached on the hoop will measure some stresses, which we might call tidal forces.

I'm not seeing tidal forces here, only uniform compression due to the regular gravitational force. Can you explain what you understand the tidal force to be?

 

[jartsa]

I'm not seeing tidal forces here, only uniform compression due to the regular gravitational force. Can you explain what you understand the tidal force to be?

Different parts of the hoop are pulled by different forces. That is a tidal force.

Well that seems grammatically wrong.

Different parts of the hoop are pulled by different forces, that is a phenomenon referred as tidal forces.@PeterDonis You see, if the "regular gravitational forces" on the hoop become larger then also the tidal forces become larger. The hoop gets compressed by a larger amount. That is why I think the other thread about weights of fast moving things is relevant.

 

[russ_watters]

Different parts of the hoop are pulled by different forces. That is a tidal force.

Well that seems grammatically wrong.

Different parts of the hoop are pulled by different forces, that is a phenomenon referred as tidal forces.

What "different parts" are you referring to? Left/right? Inside/outside? Is the hoop assumed to have non-zero thickness? Is the Earth moving through the center of the hoop?

The tidal force is a tension only, and results from adjacent parts of an object being at different distances from another object. So:

If the hoop is of small thickness compared to its distance from the central object, the tidal tension between inside and outside would be negligible. And certainly there is no scenario where it could be greater than the compression force due to its weight (like any structural arc).

If the object doesn't go through the center, there is a differential in forces between sides of the hoop, (left and right) but that isn't a tidal force either.

Perhaps you could draw a diagram of what you are envisioning?

 

[PeterDonis]

if the "regular gravitational forces" on the hoop become larger then also the tidal forces become larger

Ok, assuming this is correct (which I am not commenting on here either way, I'm just assuming it for the sake of discussion), why do you think the "regular gravitational forces" on the hoop become larger?

 

[pervect]

The Riemann tensor gives the mathematical description of the tidal forces on a body that's falling into or past a black hole.

One needs an interpretation of the tensor quantites to express them as tidal forces to get useful intuitions from the math. Following the lead of MTW, I suggest that the components of the Riemann tensor in an orthonormal basis can be interpreted as the "tidal forces". Sorry that this is so technical, I'm not sure how to translate "orthonormal basis" into terms that jartsa might recognize. It may or may not be helpful to think of creating a local coordinate system that's as nearly Minkowskii as possible over a small region, and that the Riemann tensor components in those nearly Minkowskii coordinates represent the tidal forces.

At the risk of introducing some distractions, I suppose I should mention that there are more components of the Riemann (20 independent, I believe) than there are tidal forces. But the tidal forces are among those components. I won't go into more details because it would be distracting.

With that background, we can start to address the question with calculations. The tidal forces in the direction of motion of an object falling into a black hole do not change with velocity. The transverse tidal forces, however, do change. The former statement can be found in MTW,'s text "Gravitation", which also mentions the technique of using an orthonormal basis.

Calculating the tidal forces on an object not moving into a black hole, but transverse to it (as if it were orbiting it) is also an interesting exercise, and relevant to the original quesiton, as by a change of frame of reference, one can think of the black hole as stationary, and the particle composing the "hoop" as flying past it (as opposed to falling into it).

The basic answer then is that one would indeed see tidal forces in a hoop induced by an object passing through it which would depend on the velocity of the object. Making the hoop "rigid" is problematic in these circumstances but seems to be implied by the question. One can certainly rigorously ask about the velocity pertubations in a hoop (or more generally, a cloud) of freely-floating particles) introduced by a relativistic flyby. There's a paper that discusses the velocities induced by a relativistic flyby - I"m drawing a blank on the name at the moment. The nice thing about this approach is that space-time is flat before and after the flyby, so there's no problem defining what we mean by induced velocity.

So the very short answer is that one needs to look at the directions of the tidal forces - some tidal forces components (specifically, the longitudinal tidal forces of an object falling directly into a black hole) do not change with velocity. Other components are sensitive to velocity, though.

 

[jartsa]

What "different parts" are you referring to? Left/right? Inside/outside? Is the hoop assumed to have non-zero thickness? Is the Earth moving through the center of the hoop?

Left and right side of the hoop are pulled by different forces, which I will this time call deforming forces, instead of tidal forces. The planet moves through the center of the hoop, which has a non-zero thickness.

And then there is the guy falling towards a black hole, he too is pulled into different directions by deforming forces. We are particularly interested about the difference of pulling forces on his left side and his right side. (The guy's head points up, feet point down, hands extended to the sides point to the left and to the right)

 

[pervect]

I recalled the paper I was thinking of - it was Olson & Guarino, "Measuring the active gravitational mass of a moving object", https://aapt.scitation.org/doi/10.1119/1.14280.

The detailed analysis gets complicated, but I'd like to say that in my opinion, there's reasonably justification for thinking that the stress in a hoop around the black hole increases with the black holes velocity, the biggest problem being to define exactly what congruence of worldlines represents said hoop.

However, we also have the result from MTW, where whether or not a rod is falling into a black hole or momentarily at rest with respect to the black hole does not matte to the radial component of the stress in the rod.

These results are not incompatible, it in my opinion demonstrates the need for detailed calculations.

 

[jartsa]

Why do you think this is the case?

Light with 2 joules of energy weighs two times more than light with 1 joule of energy.

Tram with 2 yotta joules of kinetic energy weighs two times more than tram with 1 yotta joules of kinetic energy, rest energy of this tram is just 1 zetta joules, and can be ignored.

So, the fast moving tram pushes the scale down so that the spring inside the scale gets compressed a lot.

See the picture here: https://www.physicsforums.com/threa...er-if-they-run-over-a-scale-very-fast.957827/

By symmetry the fast moving Earth pushes the wheels of the tram up, so that the suspension springs of the tram get compressed a lot. And by some logic we can see that the tram drivers butt compresses the springs of the seat he is sitting on a lot, which will cause the driver to say "the force of gravity is large".

I have no idea whether there is a large or small difference of force of gravity between the head of the driver and the feet of the driver.

But I know that there is a large difference of force of gravity between a driver of a very fast tram and another driver of another very fast tram at the other side of the earth. The magnitudes of the forces are large, the directions of the forces are opposite.

 

[jartsa]

the speed of the person relative to the black hole

What do you mean by this? This doesn't even look like a well-defined concept to me.

Well we can put an observer hovering near the even horizon. Then we drop some charged things side by side. The observer says the things pass him at relativistic speed. And he says that the Coulomb forces between the things are almost negated by magnetic forces.

So the observer might see two protons to be pressed together by tidal force and fuse. That sounds silly, but I'm just trying to demonstrate tidal force having a large effect on some fast falling objects.

 

[PeterDonis]

we can put an observer hovering near the event horizon.

Yes, speed relative to this observer, when infalling objects pass him, is well-defined.

Then we drop some charged things side by side. The observer says the things pass him at relativistic speed.

If they are dropped from much higher up, yes.

And he says that the Coulomb forces between the things are almost negated by magnetic forces.

Why?

 

[jartsa]

And he says that the Coulomb forces between the things are almost negated by magnetic forces.

Why?

I forgot that magnetic force between point charges is somewhat complicated, but the observer calculates that as the speed of the protons approaches c, the net electro-magnetic force between the particles, in the frame of the observer, approaches zero, the observer uses Biot-Savart law to calculate it, or whatever is the appropriate law to use.

But luckily there is another hovering observer right next to the first one, whose approach is that if the Coulomb-force in the frame of the two protons is F, then in the frame of the hovering observes the force is F/gamma. This observer has studied special relativity, and knows how forces transform between frames. This observer calculates the same net force between protons as the first observer. The calculation is just very simple.

 

[PeterDonis]

the observer calculates that as the speed of the protons approaches c, the net electro-magnetic force between the particles, in the frame of the observer, approaches zero

there is another hovering observer right next to the first one, whose approach is that if the Coulomb-force in the frame of the two protons is F, then in the frame of the hovering observes the force is F/gamma. This observer has studied special relativity, and knows how forces transform between frames. This observer calculates the same net force between protons as the first observer

But there is a third observer who is free-falling next to the protons, so with respect to this observer, the protons are at rest, at least at some instant. And therefore they have the usual Couloumb repulsion between them, and will start flying apart. This is obvious. So your argument appears to show that different observers, in different frames, will calculate different trajectories for the protons, since your observers, you claim, will calculate that the protons will come together, not fly apart.

But the protons can't do both; so either your observers or mine must be wrong. Can you give any reason why my observer's calculation should be wrong?

 

[jartsa]

But there is a third observer who is free-falling next to the protons, so with respect to this observer, the protons are at rest, at least at some instant. And therefore they have the usual Couloumb repulsion between them, and will start flying apart. This is obvious. So your argument appears to show that different observers, in different frames, will calculate different trajectories for the protons, since your observers, you claim, will calculate that the protons will come together, not fly apart.

But the protons can't do both; so either your observers or mine must be wrong. Can you give any reason why my observer's calculation should be wrong?

A proton pair falling at high speed past a hovering observer says: Coulomb force is now F and the compressing tidal force is -F, and the forces are in balance .

When the the hovering observer hears that, he says: Aha, Coulomb force is now F/gamma and the compressing tidal force is -F/gamma, and the forces are in balance.Then another proton pair falls past the hovering observer at higher speed then the previous pair. The proton pair says: Coulomb force is now F and the compressing tidal force is -2F, and I'm being crushed.

When the the hovering observer hears that, he says: Aha, Coulomb force is now F/gamma and the compressing tidal force is -2F/gamma, and the proton pair is being crushed.Note: I did not say that the tidal force increases as the speed increases, although I guess it does increase. From the point of view of the hovering observer the Coulomb force between protons decreases as speed of passing proton pairs is increased. Even if according to the hovering observer the tidal force on the protons was the same at all speeds of passing proton pairs, fast enough proton pairs would start getting together.(If we ask proton pairs, the very fast ones say they feel a very large tidal force)