Speed of gravity - simple question

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.

 

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.

 

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.

 

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

 

exp137,

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

 

Re: speed of gravity

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.

 

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".