How Fast Does Gravity Travel to a Black Hole if the Sun Vanishes?

[exponent137]

Let us suppose that we one black hole (BH) rotate around sun. Sun suddenly disappear and some time after this this black hole start to move in line. (I am interested in answer in common interpretation of general relativity, where speed of gravity is c.)
The problem is when gravity (stop) signal reach black hole, because space before and after its horizon is streched.
Probably the same question is, when sun-ray reach black hole and move it?

I please for answers.

 

[Mentz114]

The problem is when gravity (stop) signal reach black hole, because space before and after its horizon is streched.

When the sun 'disappears' the space-time around the sun's position will flatten. The flattening travels out like a wave in space-time at light speed. The BH will behave like a normal massive body in orbit.

 

[exponent137]

speed of gravity

When the sun 'disappears' the space-time around the sun's position will flatten. The flattening travels out like a wave in space-time at light speed. The BH will behave like a normal massive body in orbit.

Yes, but, what is happening close to black hole, where space is stretched?

Maybe it is clearer if we looked photon which travel from the sun toward the black hole.
If we look it (let us say that it is possible, otherwise we can choose fast moving object), we can see that as it is approaching BH horizon, he moves slower and slower. So when it will give it momentum to black hole? Of course, I believe, that it will gave it in finite time, but what is a mechanism?

The same question is for dissaperance of sun's gravity instead of photon?

 

[yuiop]

Yes, but, what is happening close to black hole, where space is stretched?

Maybe it is clearer if we looked photon which travel from the sun toward the black hole.
If we look it (let us say that it is possible, otherwise we can choose fast moving object), we can see that as it is approaching BH horizon, he moves slower and slower. So when it will give it momentum to black hole? Of course, I believe, that it will gave it in finite time, but what is a mechanism?

The same question is for dissaperance of sun's gravity instead of photon?

If the Sun suddenly disappeared then the Earth would stop following its normal orbital path after about 8 minutes which is how long it takes a photon to travel from the Sun to the Earth. Now if a smal black hole was orbiting the Sun instead of the Earth it would seem to an outside observer that it takes longer than 8 minutes for a photon to travel from the Sun to the event horizon of black hole, because of gravitational time dilation. Now if the black hole changed its orbital path 8 minutes after the Sun disappeared it would seem like the change in the gravity field reached the black hole faster than a photon could.

Hmmm.. interesting question.

 

[exponent137]

If the Sun suddenly disappeared then the Earth would stop following its normal orbital path after about 8 minutes which is how long it takes a photon to travel from the Sun to the Earth. Now if a smal black hole was orbiting the Sun instead of the Earth it would seem to an outside observer that it takes longer than 8 minutes for a photon to travel from the Sun to the event horizon of black hole, because of gravitational time dilation. Now if the black hole changed its orbital path 8 minutes after the Sun disappeared it would seem like the change in the gravity field reached the black hole faster than a photon could.

Hmmm.. interesting question.

Thanks, but it is no yet clear.
And,
1. why horizon is important as point where black hole is reached. For me, more loggicaly is radius 0.
2. For distant observer, photon or massive body never reached horizon!

 

[Jonathan Scott]

Firstly, the conservation laws of energy and momentum mean that a massive object cannot suddenly disappear, so this thread assumes an unphysical case. As far as I know, the most surprising thing that an object could do within the current laws of physics, gravitationally, is split into two equal parts which fly apart at near the speed of light with most of the rest mass converted to energy. That means that initially the total mass-energy of the two parts is the same as of the original whole, and it is only when they move far enough apart for the overall effect to be distinguishable from a single central mass that any change would be noticed.

Secondly, the idea that the black hole needs to be "told" in some way in order to change course seems to be a misconception. If the volume of space in which the black hole is moving is itself effectively being accelerated as a whole by the curvature of space-time, then the black hole will move with it.

Admittedly, if you compare the motion with some static arbitrary background "map", it appears that a change in the field could result in a change in the motion of the black hole in a way which suggested something propagating faster than the light in the vicinity of the black hole. However, this is an artifact of comparing the motion with a static map. If you compare the motion of the black hole with its surrounding space, nothing much happens at all.

 

[MeJennifer]

Firstly, the conservation laws of energy and momentum mean that a massive object cannot suddenly disappear, so this thread assumes an unphysical case. As far as I know, the most surprising thing that an object could do within the current laws of physics, gravitationally, is split into two equal parts which fly apart at near the speed of light with most of the rest mass converted to energy. That means that initially the total mass-energy of the two parts is the same as of the original whole, and it is only when they move far enough apart for the overall effect to be distinguishable from a single central mass that any change would be noticed.

The total mass-energy of two objects close together is less than if they are separated.

 

[Mentz114]

exp137,

The same question is for dissaperance of sun's gravity instead of photon?

It is not the same. Neither the behaviour of photons nor massive bodies is analogous to the space-time background changing.

Imagine a flat lake with whirlpool in it. If waves come, they will affect the whirlpool just as they affect a cork on the surface.

M

 

[exponent137]

Firstly, the conservation laws of energy and momentum mean that a massive object cannot suddenly disappear, so this thread assumes an unphysical case.

This situation was methioned because of simplification.

Secondly, the idea that the black hole needs to be "told" in some way in order to change course seems to be a misconception. If the volume of space in which the black hole is moving is itself effectively being accelerated as a whole by the curvature of space-time, then the black hole will move with it.

Admittedly, if you compare the motion with some static arbitrary background "map", it appears that a change in the field could result in a change in the motion of the black hole in a way which suggested something propagating faster than the light in the vicinity of the black hole. However, this is an artifact of comparing the motion with a static map. If you compare the motion of the black hole with its surrounding space, nothing much happens at all.

Such answer I expected. Thank you, but I will have further questions.

And similar question: when one photon (ray) gives its momentum to black hole? What is mechanism.

 

[DaveC426913]

... we can see that as it is approaching BH horizon, he moves slower and slower. So when it will give it momentum to black hole? ...

This comment by the OP seems to have been overlooked by everyone, and it may be the crux of his/her confusion.

As an object approaches a BH, it appears to slow down from the POV of an external observer. But in the object's frame of reference and the BH's FoR, time proceeds normally. Thus, there is no slowing.

 

[exponent137]

This comment by the OP seems to have been overlooked by everyone, and it may be the crux of his/her confusion.

As an object approaches a BH, it appears to slow down from the POV of an external observer. But in the object's frame of reference and the BH's FoR, time proceeds normally. Thus, there is no slowing.

Yes, I hear this. But, how to connect that one photon, which flies toward one small black hole, give it his momentum? It seems that your answer is close to my question.

 

[peter0302]

Isn't the question itself flawed, seeing as how the sun "cannot" disappear but, rather, can only move away from us, at most, at 'c'? And doesn't that fact affect the answer to any "speed of gravity" question?

 

[DaveC426913]

Isn't the question itself flawed, seeing as how the sun "cannot" disappear but, rather, can only move away from us, at most, at 'c'? And doesn't that fact affect the answer to any "speed of gravity" question?

The OP has simplified the question in an attempt to focus on the crux of his dilemma. See https://www.physicsforums.com/showpost.php?p=1788812&postcount=11".