Gravitational waves due to acceleration

[ShayanJ]

As I understood from relativity,for an accelerated object,the space-time is curved.because that curvature needs to be at the place of the object and because the object is moving,the curvature must move too, which I think is called a gravitational wave.So when an accelerated object passes near you,you should feel a moving gravitational field.
Is this correct?

Another thing is that does relativity explain how accelerated motion and energy can curve space-time?

thanks

 

[bcrowell]

The first sentence of your post sounds like an argument that an object moving with constant velocity would produce gravitational waves, which isn't true and doesn't connect logically to your second sentence. Also, note that gravitational waves can be vacuum solutions, so you don't need to talk about mass in order to explain them. This may be helpful: http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html

 

[ShayanJ]

As I understood from relativity,for an accelerated object,the space-time is curved.because that curvature needs to be at the place of the object and because the object is moving,the curvature must move too, which I think is called a gravitational wave.So when an accelerated object passes near you,you should feel a moving gravitational field.
Is this correct?

Another thing is that does relativity explain how accelerated motion and energy can curve space-time?

thanks

As you can see I mentioned an accelerated object

 

[bcrowell]

As you can see I mentioned an accelerated object

You used the word "acceleration," but your logic doesn't actually relate to acceleration.

 

[pervect]

As I recall, neither an object moving at constant velocity, nor an object with a constant acceleration, radiates gravitational waves. One needs a changing acceleration.

 

[Passionflower]

As I recall, neither an object moving at constant velocity, nor an object with a constant acceleration, radiates gravitational waves. One needs a changing acceleration.

I beg to differ.

Solutions where masses accelerate must obviously have gravitational waves. And solutions where masses are moving wrt each other will typically also generate gravitational waves.

Actually solutions that do not have any gravitational waves are more the exception than the rule in GR.

 

[Chronos]

Sounds like you are talking about Unruh radiation.

 

[PeterDonis]

I beg to differ.

Solutions where masses accelerate must obviously have gravitational waves. And solutions where masses are moving wrt each other will typically also generate gravitational waves.

Actually solutions that do not have any gravitational waves are more the exception than the rule in GR.

For solutions where more than one mass are present, they pretty much have to be moving with respect to each other, which means that their accelerations will be changing, so they meet pervect's criterion.

For solutions with a single massive object accelerating, if the object is accelerating in a perfectly straight line, I don't believe gravitational waves will be produced. For example, I don't believe the Kinnersley Photon Rocket solution has any gravitational waves.

 

[PeterDonis]

I should probably also point out that I switched usages of the word "acceleration" in my last post. A solution with two masses orbiting about their mutual center of mass (for example, a binary pulsar) does radiate gravitational waves, even though both objects are in free fall--they are "accelerated" only in the sense of coordinate acceleration in, for example, the rest frame of the center of mass of the system. So "acceleration" in the coordinate-independent sense (proper acceleration) is not required to produce gravitational waves.

The Kinnersley Photon Rocket, on the other hand, describes an object with proper acceleration (i.e., "accelerated" in the coordinate-independent sense), caused by emitting an "exhaust" of electromagnetic radiation out the back. So (if I'm right that there are no gravitational waves in this solution) the presence of proper acceleration is not sufficient to produce gravitational waves.

 

[bcrowell]

Solutions where masses accelerate must obviously have gravitational waves.

This is incorrect. The power radiated in gravitational waves is proportional to $(d^3Q/dt^3)^2$. Therefore masses that accelerate need not emit gravitational waves. As a concrete example, if two parallel sheets of mass fall toward one another, no gravitational radiation is emitted (in the semi-Newtonian limit), because each sheet's acceleration is constant, so $d^3Q/dt^3=0$. The $(d^3Q/dt^3)^2$ variation is analogous to the behavior of electric quadrupole radiation in E&M.

 

[Passionflower]

(in the semi-Newtonian limit)

Huh? Are you trying to pull the wool here?

Please show me one static solution where masses accelerate.

 

[pervect]

The Kinnersley Photon Rocket, on the other hand, describes an object with proper acceleration (i.e., "accelerated" in the coordinate-independent sense), caused by emitting an "exhaust" of electromagnetic radiation out the back. So (if I'm right that there are no gravitational waves in this solution) the presence of proper acceleration is not sufficient to produce gravitational waves.

Yes, the Kinnersley photon rocket was one of the sources I had in mind.
http://prola.aps.org/abstract/PR/v186/i5/p1335_1

While I couldn't find the text online, http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909087v2.pdf covers much of the same material - but with a different focus.

http://arxiv.org/abs/gr-qc/9412063 has some interesting things to say on the topic and is also online.

Appareantly the Kinnersley rocket never radiates, though, even for a "jerky" acceleration profile, which wasn't how I recalled things. I have a feeling I'm missing something, somewhere, though it is clear that gravitational radiation is approximately proportional to the square of the third derivative of the quadrople moment.

 

[Passionflower]

I should probably also point out that I switched usages of the word "acceleration" in my last post. A solution with two masses orbiting about their mutual center of mass (for example, a binary pulsar) does radiate gravitational waves, even though both objects are in free fall--they are "accelerated" only in the sense of coordinate acceleration in, for example, the rest frame of the center of mass of the system. So "acceleration" in the coordinate-independent sense (proper acceleration) is not required to produce gravitational waves.

You are turning it upside down now, that is not what I wrote about.

I wrote that in a solution where one or more masses undergo proper acceleration we must have to do with gravitational waves.

I am really at a loss why folks keep spinning things here, for what purpose? Face saving? Sorry folks but this is a real waste of time. Clearly the topic is about proper acceleration of masses.

 

[espen180]

In GR the orbit of binary masses will decay over time, and I recall reading that energy is thought to be leaked from the system in the form of gravitational waves.

 

[PeterDonis]

You are turning it upside down now, that is not what I wrote about.

I wrote that in a solution where one or more masses undergo proper acceleration we must have to do with gravitational waves.

That's why I went back and clarified--because, unlike the solutions with masses in orbit (which I agree are not relevant to the OP, since all the masses are in free fall--though it is interesting that in such a case, with no proper acceleration, there can still be gravitational waves), the Kinnersley Photon Rocket is a solution where we have a mass undergoing *proper* acceleration, but there are *no* gravitational waves.

 

[bcrowell]

Please show me one static solution where masses accelerate.

This doesn't have anything to do with my post. My post was pointing out the error in the following statement:

Solutions where masses accelerate must obviously have gravitational waves.

I gave a counterexample where masses do accelerate and don't emit gravitational radiation.

I wrote that in a solution where one or more masses undergo proper acceleration we must have to do with gravitational waves.

This is incorrect. Proper acceleration is neither necessary nor sufficient. It's not necessary, because both the neutron stars in the Hulse-Taylor system have zero proper acceleration (they're both free-falling), but the system radiates. It's not sufficient, because a system can contain masses that have nonzero proper acceleration and yet the system can not radiate. For example, you could have a spherically symmetric system in which lots of mass is subject to proper accelerations, but it wouldn't radiate, because $d^3Q/dt^3$ would be zero.

 

[Passionflower]

This is incorrect. Proper acceleration is neither necessary nor sufficient.

Where did I claim proper acceleration is necessary?

It's not sufficient, because a system can contain masses that have nonzero proper acceleration and yet the system can not radiate.

You still have not given a solution where this is the case.

 

[bcrowell]

Where did I claim proper acceleration is necessary?

You didn't, but you have claimed that proper acceleration has some relevance to the question of whether something will radiate. I've pointed out that it has no such relevance, since it is neither necessary nor sufficient.

You still have not given a solution where this is the case.

I did. See #16.

 

[Passionflower]

You didn't, but you have claimed that proper acceleration has some relevance to the question of whether something will radiate. I've pointed out that it has no such relevance, since it is neither necessary nor sufficient.I did. See #16.

Then give me one single reference in the literature that deals with a solution related to what you suggested here:

For example, you could have a spherically symmetric system in which lots of mass is subject to proper accelerations, but it wouldn't radiate, because d^3Q/dt^3 would be zero.

 

[pervect]

One counterexample should be sufficient, but Kinnersley's photon rocket, and Bonnor's as well also serve as counter examples - they are accelerating rockets that don't emit gravitational waves.

Google or a review of the thread should easily find the reference for the former, for Bonnor's photon rocket see:

http://iopscience.iop.org/0264-9381/13/2/015

 

[Passionflower]

One counterexample should be sufficient, but Kinnersley's photon rocket, and Bonnor's as well also serve as counter examples - they are accelerating rockets that don't emit gravitational waves.

Google or a review of the thread should easily find the reference for the former, for Bonnor's photon rocket see:

http://iopscience.iop.org/0264-9381/13/2/015

And the mass of those rockets is?

 

[pervect]

The rockets are massive - they are called "photon rockets" because the rocket exhaust is null dust.

 

[bcrowell]

Then give me one single reference in the literature that deals with a solution related to what you suggested here:

For example, you could have a spherically symmetric system in which lots of mass is subject to proper accelerations, but it wouldn't radiate, because d^3Q/dt^3 would be zero.

Birkhoff, Relativity and Modern Physics, 1923, p. 244 proves that no spherically symmetric spacetime can include gravitational radiation. A real-world example would be that an isolated, spherically symmetric star does not radiate gravitational waves, even though all of its mass is subject to large proper accelerations.

 

[PAllen]

As you can see I mentioned an accelerated object

One thing that may clarify this (perhaps also answer some of Passionflower's questions) is that the force experienced by a test particle from a moving massive body tracks the instantaneous position of the massive body (as if there were no lightspeed delay) as long as the body's motion does is uniform OR uniformly accelerating. Only if the massive body undergoes changing acceleration does the test body feel a force that lags the 'instantaneous position' of the body, making finite propagation speed of gravity manifest. Further, it is only when such a lag occurs that momentum and energy conservation require gravitational radiation. (Of course, the test body isn't really detecting the instantaneous position of of the massive body, it is simply feeling a force directed to the quadratically extrapolated position of the massive body).

The following discusses all of this:

http://arxiv.org/abs/gr-qc/9909087

 

[George Jones]

For solutions with a single massive object accelerating, if the object is accelerating in a perfectly straight line, I don't believe gravitational waves will be produced. For example, I don't believe the Kinnersley Photon Rocket solution has any gravitational waves.

Interestingly, it seems that it took 25 years to recognize the lack of gravitational radiation.

From Exact Space-Times in Einstein's General Relativity by Griffiths and Podolsky

... Bonner (1994) found, quite surprisingly, that with respect to the natural flat background frame there is no energy loss corresponding to gravitational radiation emitted by the accelerating rocket. ... subsequently confirmed by Damour (1995) ... he argued that ... In fact, the radiation is the sum of waves generated by the point-like rocket and of those generated by the photon fluid. To the highest order, these two distinct contributions cancel each other ... Further studies of this effect have been undertaken by Dain, Moreschi and Geiser (1996) ... von der Gonna and Kramer (1998) ... confirmed by Cornish (2000) even without the assumption of axial symmetry

pervect gave a link to Damour (1995) in post #12.

One counterexample should be sufficient, but Kinnersley's photon rocket, and Bonnor's as well also serve as counter examples - they are accelerating rockets that don't emit gravitational waves.

Google or a review of the thread should easily find the reference for the former, for Bonnor's photon rocket see:

http://iopscience.iop.org/0264-9381/13/2/015

Bonner's claim that his rocket does not radiate gravitationally has generated some controversy.

Bonner (1996) has observed that such photon rockets with $\Lambda = 0$ lose no energy as gravitational radiation, However, this is in disagreement with later results obtained by von der Gonna and Kramer (1998) ... subsequently extended by Cornish (2000)

All of the above show that issues in general relativity can be quite subtle.

 

[atyy]

"with respect to the natural flat background frame"

Why is that the natural background frame?

So, is it that the radiation at higher orders does not cancel? Or is it simply controversial still?