Explanation of why there can't be dipole gravitational radiation

In summary, the conversation discusses the concept of gravitational radiation and its relation to the conservation of energy and momentum. It is argued that the MTW expression for the dipole moment in terms of masses is a simple Newtonian approximation and does not take into account other forms of energy and momentum, including gravitational. Therefore, it is not possible to create dipole radiation in a system. However, there is a question about the possibility of dipole radiation in certain scenarios, such as the asymmetric collision of two black holes. The conversation also delves into the analogy with electromagnetism and the potential effects of a charged particle in a gravitational system. Overall, there is a need for more research and insights on this topic.
  • #1
Jonathan Thornburg -- remove -animal to reply
[[disclaimer: this is *not* a homework assignment]]

In general relativity, the lowest non-vanishing multiple of gravitational
radiation is generically the quadrupole: the monopole is forbidden
by Birkhoff's theorem, and conservation of momentum is forbidden by
conservation of momentum. I thought I understood this latter argument
(set out in Misner, Thorne, and Wheeler section 36.1)... but in
discussing this point with a colleague, I've become less certain
that I understand it.

To focus the discussion, let's consider the asymmetric collision of
two stars (merging to form a bigger star), and let's suppose the system
is *not* relativistic, i.e. let's suppose that Newtonian gravity/mechanics
provide a good approximation to the dynamics. MTW's argument simply
says that any change in the mass dipole moment of the system would
violate conservation of linear momentum.

The problem is, gravitational radiation can carry linear momentum,
and the MTW formula only applies to the dipole moment of the *masses*
in the system. How do I know that the system can't emit dipole
gravitational radiation, with the final merged stars recoiling in
the opposite direction so that the total linear momentum of the
mass+gravitational-radiation system is conserved?

To look at the issue from a slightly different perspective, let's
look at standard quadrupolar gravitational radiation. We know that
an asymmetric star collision radiates quadrupole gravitational radiation
which (in general) *does* carry a net linear momentum, with the merged
star recoiling in the opposite direction. How do I know that this
can't also apply to dipole gravitational radiation?

Just to make matters more interesting, suppose we now drop the
Newtonian-gravity approximation, and consider (say) the asymmetric
collision of two black holes. In this case it's known from numerical
simulations that asymmetric collisions generally radiate a net linear
momentum in (quadrupole) gravitational radiation (see, eg, Sperhake
et al, Physical Review Letters 98, 091101). How do I now that this
isn't also the case for dipole gravitational radiation?

Can anyone offer any insights here?

thanks, ciao,

--
-- "Jonathan Thornburg -- remove -animal to reply" <jthorn@aei.mpg-zebra.de>
School of Mathematics, U of Southampton, England
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam
 
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  • #2
On 3 Apr, 19:21, "Jonathan Thornburg -- remove -animal to reply"
<jth...@aei.mpg-zebra.de> wrote:
> ...
> The problem is, gravitational radiation can carry linear momentum,
> and the MTW formula only applies to the dipole moment of the *masses*
> in the system. How do I know that the system can't emit dipole
> gravitational radiation, with the final merged stars recoiling in
> the opposite direction so that the total linear momentum of the
> mass+gravitational-radiation system is conserved?


The MTW expression for the dipole moment in terms of masses is a
simple Newtonian approximation; exact conservation of energy and
momentum would require it to include all other forms of energy and
momentum within the system, including gravitational. That means that
regardless of what is happening in the system (including any higher
order multipole gravitational radiation) it is not possible to move
the center of mass of the system as a whole, and hence it is not
possible to create dipole radiation.

Jonathan Scott (Chandlers Ford, near Southampton, England)
 
  • #3
Hi this (old) topic interest me a lot. I am not sure to understand what you say correctly. Because it is not possible to move the center of mass, ok, but there exist a "frame" where radiation carry energy, thus it should be possible to see the same center of mass/energy no? I explain myself: In this reference frame for example, a small body falling onto a big body will acelerate a lot. If I take the analogy with electromagnetism, what we call dipolar radiation, is not only really the dipolar one, but also the "late part" of electromagnetic field, in 1/r that also comes from a sole accelerating charge. Why a small body falling on a big shouldn't radiate, or more accurately have the same 1/r part? We don't speak about point test particle here, and carrying on the analogy with electromagnetism, a small body accelerating a lot radiates (so loses) more energy than a big accelerating just a little. This is why some accelerators use protons instead of neutrons. So maybe the small body will lose more energy than the big one, and the retroaction should be more important. I guess this is the question, the center of mass doesn't look to change in a quadrupolar radiation, it doesn't seem to hange in a two body system orbiting, but bodies don't follow geodesics.
In electromagnetism the energy is slightly radiate in front of the charge, factor depending on the relative speed of the charge to the observer. So are you definitely totally sure there shouldn't be a radiation?


Second, let's imagine two equal masses, one charged, the other not. Maybe the charged one would radiate from a far perspective while falling on the body, or the equivalence principle prevent it from losing energy by electromagnetic radiation?

If it radiates electromagnetic radiations, then the repelling that comes from self interaction should slow down the charged particle, and the other could radiate gravitationally more because it would accelerate more, or then the center of mass/energy should change.

Sorry for the english, I am french.
 
  • #4
I read more carefully what you said, and I think I understood, sorry... So there are gravitationnal dipolar radiations, IF we don't take it as a part of the stress energy tensor source? Am I right?
 
  • #5


Dear Jonathan Thornburg,

Thank you for bringing up this interesting and thought-provoking question. I would like to provide a response to your queries and offer some insights on why there cannot be dipole gravitational radiation.

Firstly, let us clarify the concept of dipole gravitational radiation. In general relativity, gravitational radiation is described by the Einstein field equations, which predict the emission of gravitational waves due to the acceleration of massive objects. These waves carry energy, momentum, and angular momentum away from the source and can be characterized by their multipole moments, which represent different orders of symmetry. The lowest non-vanishing multiple of gravitational radiation is the quadrupole, as you have correctly stated. This means that dipole gravitational radiation, which would correspond to a change in the mass dipole moment of the system, is forbidden by the equations of general relativity.

Now, let us consider the conservation of linear momentum in the context of asymmetric star collisions. As you have pointed out, the system can emit quadrupole gravitational radiation, which carries a net linear momentum, causing the merged star to recoil in the opposite direction. However, this does not violate conservation of linear momentum because the total linear momentum of the system, including the gravitational radiation, is conserved. This is because the gravitational radiation carries a negative momentum, which cancels out the positive momentum of the merged star.

In the case of dipole gravitational radiation, the situation is different. As mentioned earlier, dipole gravitational radiation is forbidden, so the system cannot emit such radiation. Therefore, the total linear momentum of the system, including the gravitational radiation, remains unchanged, and conservation of linear momentum is not violated.

Finally, in the case of asymmetric collisions of black holes, the numerical simulations you have mentioned also show that the system emits quadrupole gravitational radiation, which carries a net linear momentum. This is consistent with the general relativity predictions and does not indicate the presence of dipole gravitational radiation.

In conclusion, the reason why there cannot be dipole gravitational radiation is that it is forbidden by the equations of general relativity. The conservation of linear momentum is not violated because the gravitational radiation carries a negative momentum, which cancels out the positive momentum of the system. I hope this response has provided some insights into this interesting topic. Thank you for your question.

Sincerely,
 

1. What is dipole gravitational radiation?

Dipole gravitational radiation is a hypothetical type of radiation that would occur if a system with a changing mass quadrupole moment also had a changing mass dipole moment. This type of radiation has not been observed in nature and is not predicted by Einstein's theory of general relativity.

2. Why can't there be dipole gravitational radiation?

According to Einstein's theory of general relativity, gravitational radiation is only produced by systems with a changing mass quadrupole moment. This means that the mass distribution of the system must be changing in a non-symmetric way. A changing mass dipole moment would not produce gravitational radiation because it does not cause a change in the mass distribution of the system.

3. Can dipole gravitational radiation be detected?

No, dipole gravitational radiation cannot be detected because it does not exist according to our current understanding of gravity. It is not predicted by Einstein's theory of general relativity and has not been observed in any natural phenomena.

4. Are there any implications for astrophysics if dipole gravitational radiation does exist?

If dipole gravitational radiation were to exist, it would have significant implications for our understanding of gravity and astrophysics. It would require a new theory of gravity and could potentially change our understanding of the behavior of massive objects in the universe.

5. Is there ongoing research on dipole gravitational radiation?

No, there is currently no ongoing research on dipole gravitational radiation because it is not a supported concept in modern physics. However, scientists are continually studying and refining our understanding of gravity, so it is possible that new discoveries could lead to a better understanding of this phenomenon in the future.

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