Warped spacetime around BH and the barycenter

[Robittybob1]

I was looking at the way they draw BHs merging and I think are they drawing it wrong.

If things orbit along a geodesic how can they draw the spacetime curvature as two pits. Do the BHs have a common center of mass (the barycenter) and shouldn't that point be the deepest part of the warp?

[swansont]

I was looking at the way they draw BHs merging and I think are they drawing it wrong.

If things orbit along a geodesic how can they draw the spacetime curvature as two pits. Do the BHs have a common center of mass (the barycenter) and shouldn't that point be the deepest part of the warp?

 

Why would it be? Consider two BHs approacing each other. Far away, the curvature has to be centered on each BH. Why would it suddenly shift to the CoM?

[Robittybob1]

Why would it be? Consider two BHs approacing each other. Far away, the curvature has to be centered on each BH. Why would it suddenly shift to the CoM?

That is a point, but how do they orbit along a geodesic if it doesn't? [error corrected] It has me baffled ATM.

Struggling to find anything that covers it, but I'm thinking could the two gravity wells merge at the outer edges where the orbiting bodies each orbit along a geodesic partly formed by the other body???

 

In this view a body's own mass does not drastically change the shape of the gravity well formed by the body it is orbiting. Could this be the answer? But when they look at the Solar System Barycenter everything is orbiting that point so the shape of the geodesic is definitely reshaped by a body's own mass too.

So instead of drawing the BHs in the center of their gravity wells (prior to their merger) they are really traveling along the wall (the geodesic) of the reshaped gravity well of the combined mass. This shape still has two deep impressions but the bodies are on the sides of the combined impression (not strictly centered on it own gravity well).

I wonder if we can find a paper that backs this idea up?

 

[if that is too speculative please move the thread to speculations.]

Edited March 9, 2016 by Robittybob1

[Strange]

That is a point, but how do they orbit a geodesic if it doesn't?

They don't orbit a geodesic. The paths they travel on, like any body in free fall, is a geodesic.

 

Struggling to find anything that covers it, but I'm thinking could the two wells merge at the edges where they each orbit along a geodesic partly formed by the other body?

Some of the simulations (particularly the one I posted before: http://cplberry.com/2015/09/12/monty-carla/) have representations of the curvature of space-time around the merging black holes.

 

I wonder if we can find a paper that backs this idea up?

No.

Edited March 9, 2016 by Strange

[Robittybob1]

 

They don't orbit a geodesic. The paths they travel on, like any body in free fall, is a geodesic.

 

 

Some of the simulations (particularly the one I posted before: http://cplberry.com/2015/09/12/monty-carla/) have representations of the curvature of space-time around the merging black holes.

 

 

No.

That was sloppy speech, I meant "orbit along a geodesic", not "orbit a geodesic". Thanks for correcting that.

I would have liked to check your link but it doesn't work.

Well early days yet.

There are no scientific papers or Youtube videos detailing how the barycenter of orbiting bodies relates to the spacetime curvature.

 

Is this a new law? "Bodies in orbit travel along a geodesic of the gravity well of the combined mass orbiting around the barycenter. This shape overall still has two or more deep impressions (spacetime curvatures associated with the mass of the bodies, but the bodies are orbiting along the geodesics of the combined spacetime curvature (which is not strictly centered on its own gravity well)".

 

Edit: Not centered on the barycenter for the barycenter is not the center but the point of rotation.

Edited March 9, 2016 by Robittybob1

[Strange]

I would have liked to check your link but it doesn't work.

 

Fixed.

 

There are no scientific papers or Youtube videos detailing how the barycenter of orbiting bodies relates to the spacetime curvature.

Searching for general relativity barycenter on Google scholar produces 17,000 results. I have no idea if any of them describe what you want to know.

[Robittybob1]

 

Fixed.

 

Searching for general relativity barycenter on Google scholar produces 17,000 results. I have no idea if any of them describe what you want to know.

I'm working my way through Google search at this stage. So far no luck at page 4. Only one site began to discuss it but the site was titled "Einstein was wrong".

I've given up with Google search. I've already checked Google Scholar but I was using a different set of words.

spacetime + curvature + barycenter the words "general relativity" would produce just too many results.

spacetime + curvature + barycenter + geodesic no good results after the first 10 pages.

@Strange - That link is still not working could you give me the title or 10 words in the article and I'll find it through Google. Thanks.

Edited March 9, 2016 by Robittybob1

[Strange]

Here it is again: http://cplberry.com/2015/09/12/monty-carla/

 

It is a blog post called "LIGO Magazine: Issue 7" by Christopher Berry, "Gravitational Wave Astronomer" (so I guess he knows what he is talking about!)

[Robittybob1]

Here it is again: http://cplberry.com/2015/09/12/monty-carla/

 

It is a blog post called "LIGO Magazine: Issue 7" by Christopher Berry, "Gravitational Wave Astronomer" (so I guess he knows what he is talking about!)

Interesting animations but didn't show what I am trying to say here. I need an animation where the curvature and the BH are in contact. It is just too complex and I can't do the animations myself.

[swansont]

 

Is this a new law? "Bodies in orbit travel along a geodesic of the gravity well of the combined mass orbiting around the barycenter. This shape overall still has two or more deep impressions (spacetime curvatures associated with the mass of the bodies, but the bodies are orbiting along the geodesics of the combined spacetime curvature (which is not strictly centered on its own gravity well)".

 

 

 

It's more like an old observation than a new law, AFAICT.

[Strange]

Interesting animations but didn't show what I am trying to say here.

 

It may not show what you are trying to say because what you are trying to say is wrong.

 

 

I need an animation where the curvature and the BH are in contact.

 

What does that mean? That animation pauses (at about 0:50) when the black holes are in contact. It shows that at that point, not surprisingly, the curvature of space-time also merges.

 

It is just too complex and I can't do the animations myself.

 

Of course you can't. These take hours (probably days) of supercomputer time.

[Robittybob1]

 

 

It's more like an old observation than a new law, AFAICT.

True, but it is so difficult to get a scientific statement with the words barycenter, warped spacetime and orbit in it. It is an "old observation" an old idea that has never been written.

Does that mean you see what I'm trying to say? Whereas Strange is keeping on saying I'm wrong without providing a reason.

 

It may not show what you are trying to say because what you are trying to say is wrong.

 

 

What does that mean? That animation pauses (at about 0:50) when the black holes are in contact. It shows that at that point, not surprisingly, the curvature of space-time also merges.

 

It is just too complex and I can't do the animations myself.

 

Of course you can't. These take hours (probably days) of supercomputer time.

A series of stills would suffice. When you ask "It may not show what you are trying to say because what you are trying to say is wrong" are you saying it maybe wrong which allows it maybe right as the alternative? I could be right or I could be wrong!

Why would it be wrong?

Binaries orbit their barycenter, orbiting bodies follow their geodesics through curved spacetime. Implies there is some connection between the curved spacetime and the barycenter. With GE being lost they are descending into their curved spacetime wells (falling and losing the PE) continuously and increasingly but at the same time orbiting their barycenter. It is a more complex animation but not one that would be impossible to represent.

Edited March 9, 2016 by Robittybob1

[Strange]

I find some of your statements (like your new "law") very hard to parse and so can't really comment on them.

 

The simulations I provided show that the claim you originally made (that the curvature or gravity well was greatest at the barycenter) is wrong. But you seem to have moved on from there (I'm just not quite sure where to!)

 

I think the reason you might have trouble find what you are looking for is because the barycentre is a concept from Newtonian dynamics and,as I think Mordred has already said, solving for two bodies orbiting each other in GR is non-trivial. Which is why it requires simulation on supercomputers. As such, I suspect it is not easy to derive the concept of a barycentre in GR. But, when you simulate the behaviour, you find the bodies do orbit their common centre of gravity (aka barycentre).

[Robittybob1]

I find some of your statements (like your new "law") very hard to parse and so can't really comment on them.

 

The simulations I provided show that the claim you originally made (that the curvature or gravity well was greatest at the barycenter) is wrong. But you seem to have moved on from there (I'm just not quite sure where to!)

 

I think the reason you might have trouble find what you are looking for is because the barycentre is a concept from Newtonian dynamics and,as I think Mordred has already said, solving for two bodies orbiting each other in GR is non-trivial. Which is why it requires simulation on supercomputers. As such, I suspect it is not easy to derive the concept of a barycentre in GR. But, when you simulate the behaviour, you find the bodies do orbit their common centre of gravity (aka barycentre).

I went past my original question once Swansont pointed out the error, but I came up with the final version later. I hope you were not stuck with the original idea which was patently wrong.

I'm not claiming this as my new law or anything, it might be old as the hills as Swansont implies.

 

You've nearly got it! Orbiting their barycenter, falling along their curved spacetime geodesics and radiating GE all at the same time.

All in the one image.

I didn't like the animation in the video in the OP because the BHs were centered on their own gravity wells but they ought to be on the curved spacetime surface formed by the binary and itself. That means they should have been further out and not above their own gravity wells.

Even that may be wrong. It could be a type of rotation i.e like the gravity wells having their deepest parts pointing somewhat toward the barycenter. It is hard to describe. But it could be something like the cups on a centrifuge rotating outward as the speed increases, but in the opposite direction. With BH mergers the gravity wells maybe be pointing increasingly inward (not outward) as the speed increases.

Now that is definitely a new idea.

 

For what I have been trying to find is the connection between Einstein's prediction of gravitational radiation and the reason he predicted gravitational radiation. If you ever see the reason he predicted it please let me know.

Edited March 9, 2016 by Robittybob1

[swansont]

 

Binaries orbit their barycenter, orbiting bodies follow their geodesics through curved spacetime. Implies there is some connection between the curved spacetime and the barycenter.

 

 

It's not obvious to me that this would be true.

 

Any binary acts this way, so you have a whole continuum of possible curvatures of the spacetime.

[Janus]

I was looking at the way they draw BHs merging and I think are they drawing it wrong.

If things orbit along a geodesic how can they draw the spacetime curvature as two pits. Do the BHs have a common center of mass (the barycenter) and shouldn't that point be the deepest part of the warp?

No, the barycenter would not be the deepest part. You have to consider what the drawing represents. The "depth" represents gravitational potential. The slope would be the gravitational acceleration at that point.

 

So let's look at a typical diagram of two nearby equal masses. Here, black represents flat space-time far from a gravity source, and the brighter the red, the lower the gravity potential.

 

 

Here the barycenter is halfway between the masses and is on the "saddle" between the dips. It is at a lower potential than the surrounding flat space, so far off objects would tend to fall towards it. However, it also slopes off in both directions towards the masses. Now at the lowest point of the saddle, the slope flattens out to zero. So an object placed right there would be at zero g and not tend to fall towards either body. However, this is not a very stable position as the slightest nudge will start it falling towards one or the other body.

The point is that the barycenter here is not the deepest point because you have to do work against gravity to get there from either mass. Neither is the barycenter tied to this saddle point. If I were to redraw this graph we one mass twice that of the other, the saddle would shift towards the smaller mass and the barycenter towards the larger mass.

 

Here is a more practical example of why the barycenter is not the deepest point. Remembering that the deepest point is where things are more likely to settle, and where gravity tends to point, consider the Earth-Moon barycenter. It is a little below the surface of the Earth. If it was the lowest gravity potential and where gravity tended to point, then it would be the overriding factor in determining the direction of down for people on the Earth. IOW, down would not point towards the center of the Earth, but to this point just a bit under the surface of the Earth in the direction of the Moon.

Since this is not the case, this is a good indicator that the Earth-Moon barycenter is not the the lowest point of gravitational potential.

[Robittybob1]

 

 

It's not obvious to me that this would be true.

 

Any binary acts this way, so you have a whole continuum of possible curvatures of the spacetime.

The idealised spacetime curvature is drawn as if the body is in deep space. When it is in a binary orbit I imagine the curvature is a combination of the two. If there were n-bodies it is very complex. So I don't have a problem with that idea ("whole continuum of possible curvatures of the spacetime") but don't ask me to draw it.

Read #14 as it was edited.

Edited March 9, 2016 by Robittybob1

[Strange]

That means they should have been further out and not above their own gravity wells.

Even that may be wrong.

 

It is patently wrong. The animation I posted recently is produced by someone working on LIGO. I have no reason not to believe it is not accurate. Also, the amount of curvature of space-time is related to the mass-energy at that point, not somewhere else.

 

For what I have been trying to find is the connection between Einstein's prediction of gravitational radiation and the reason he predicted gravitational radiation. If you ever see the reason he predicted it please let me know.

 

Here: http://articles.adsabs.harvard.edu/cgi-bin/get_file?pdfs/SPAW./1918/1918SPAW.......154E.pdf

 

A bit of background here: http://www.hs.uni-hamburg.de/DE/GNT/events/pdf/steinicke05.pdf

 

Does that help?

[Robittybob1]

No, the barycenter would not be the deepest part. You have to consider what the drawing represents. The "depth" represents gravitational potential. The slope would be the gravitational acceleration at that point.

 

So let's look at a typical diagram of two nearby equal masses. Here, black represents flat space-time far from a gravity source, and the brighter the red, the lower the gravity potential.

 

 

Here the barycenter is halfway between the masses and is on the "saddle" between the dips. It is at a lower potential than the surrounding flat space, so far off objects would tend to fall towards it. However, it also slopes off in both directions towards the masses. Now at the lowest point of the saddle, the slope flattens out to zero. So an object placed right there would be at zero g and not tend to fall towards either body. However, this is not a very stable position as the slightest nudge will start it falling towards one or the other body.

The point is that the barycenter here is not the deepest point because you have to do work against gravity to get there from either mass. Neither is the barycenter tied to this saddle point. If I were to redraw this graph we one mass twice that of the other, the saddle would shift towards the smaller mass and the barycenter towards the larger mass.

 

Here is a more practical example of why the barycenter is not the deepest point. Remembering that the deepest point is where things are more likely to settle, and where gravity tends to point, consider the Earth-Moon barycenter. It is a little below the surface of the Earth. If it was the lowest gravity potential and where gravity tended to point, then it would be the overriding factor in determining the direction of down for people on the Earth. IOW, down would not point towards the center of the Earth, but to this point just a bit under the surface of the Earth in the direction of the Moon.

Since this is not the case, this is a good indicator that the Earth-Moon barycenter is not the the lowest point of gravitational potential.

@Janus - Where did you get that neat picture from? It is amazing thanks.

 

Note the original question in the OP had been answered and I accept the answer was "no". I now accept that the barycenter is not the deepest part of the gravity well, even though it is sometimes called the center of mass.

"Here the barycenter is halfway between the masses and is on the "saddle" between the dips." That bit is a little wrong especially if the mass at the rear is more massive. Like the Earth-Sun barycenter is definitely inside the Sun's mass.

 

But the rest sounds very correct.

If those two masses were orbiting could you show that each followed a geodesic?

 

It is patently wrong. The animation I posted recently is produced by someone working on LIGO. I have no reason not to believe it is not accurate. Also, the amount of curvature of space-time is related to the mass-energy at that point, not somewhere else.

....

I'm not saying they made a terrible mistake or something like that.

If you say "the amount of curvature of space-time is related to the mass-energy at that point, not somewhere else" that is fair enough but does that not also imply the introduction of another mass nearby will influence the amount of curvature of space-time for the mass-energy at that point has changed?

 

....

 

Here: http://articles.adsabs.harvard.edu/cgi-bin/get_file?pdfs/SPAW./1918/1918SPAW.......154E.pdf

 

A bit of background here: http://www.hs.uni-hamburg.de/DE/GNT/events/pdf/steinicke05.pdf

 

Does that help?

No it doesn't

Edited March 9, 2016 by Robittybob1

[Janus]

@Janus - Where did you get that neat picture from? It is amazing thanks.

I whipped it up with 3-D modeling program.

 

Note the original question in the OP had been answered and I accept the answer was "no". I now accept that the barycenter is not the deepest part of the gravity well, even though it is sometimes called the center of mass.

"Here the barycenter is halfway between the masses and is on the "saddle" between the dips." That bit is a little wrong especially if the mass at the rear is more massive. Like the Earth-Sun barycenter is definitely inside the Sun's mass.

 

 

Note that I said "here", as in in this particular instance where the masses were equal. I also went on to say that this would not be the case if the masses were not equal. So there was nothing "wrong" with the statement when taken in context.

[Robittybob1]

 

@Janus - Where did you get that neat picture from? It is amazing thanks.

I whipped it up with 3-D modeling program.

 

Note the original question in the OP had been answered and I accept the answer was "no". I now accept that the barycenter is not the deepest part of the gravity well, even though it is sometimes called the center of mass.

"Here the barycenter is halfway between the masses and is on the "saddle" between the dips." That bit is a little wrong especially if the mass at the rear is more massive. Like the Earth-Sun barycenter is definitely inside the Sun's mass.

 

 

Note that I said "here", as in in this particular instance where the masses were equal. I also went on to say that this would not be the case if the masses were not equal. So there was nothing "wrong" with the statement when taken in context.

 

Sorry, I might have misunderstood you as I thought you were referring to the picture which seems to suggest that the mass at the rear is larger. But yes if the masses were equal the barycenter would be in the center of the saddle. My mistake.

Edited March 9, 2016 by Robittybob1

[Robittybob1]

.....

With BH mergers the gravity wells maybe be pointing increasingly inward (not outward) as the speed increases.

Now that is definitely a new idea.

.....

In that paper Strange linked to there was a scene at the end of it where the two black holes merge into each other. I'll put a link to it

http://cplberry.com/2015/09/12/monty-carla/ the section of interest

till the end.

@Strange did you understand why they added that bit to the end of the BH merger animation?

[Strange]

I assume it is there just to make it clearer what happens to the event horizons as the black holes approach one another - by removing the orbital motion, it is easier to see how they distort and merge.

[Robittybob1]

That section had the title "Black hole head-on collision" I would think if 2 black holes were to collide head on it would be a lot more dramatic than that. The orbital motion definitely slows the infall compared to free fall. There is a timer on the screen is that in seconds? Finishes on 44:0 maybe it is in milliseconds?

[Strange]

That section had the title "Black hole head-on collision" I would think if 2 black holes were to collide head on it would be a lot more dramatic than that. The orbital motion definitely slows the infall compared to free fall.

 

That is only showing the changes to the event horizons. There is a lot more going on that is not shown there. For example: https://www.caltech.edu/news/physicists-discover-new-way-visualize-warped-space-and-time-1680

 

There is some more background on the simulations here: http://calteches.library.caltech.edu/711/2/BlackHoles.pdf

Note that simulating a single, stationary black hole took something like 24 hours on 52,000 processors. This is definitely non-trivial stuff.

 

There is a whole website dedicated to these simulations and related research: http://www.black-holes.org/