Do not believe this letter on gravitational radiation

[cellotim]

I was looking for references on the quadrupolar formula and found this http://adsabs.harvard.edu/full/1992Ap&SS.194..159Y". I was so shocked to find that it had actually been published (although it was nearly 20 years ago) that I had to post this warning that there is a fundamental flaw in the paper.

In the paper, the author discusses the quadrupolar formula which has been used to derive the orbital speed-up of a binary star system. This orbital speed-up has been measured with good accuracy for the binary pulsar system PSR 1913 + 16. The author then goes on to try to demonstrate that the energy loss is zero through a gross misuse of the continuity equation for the linearized Einstein equations, $$\partial_\mu T^{\mu\nu} = 0$$. In fact, the author assumes that the continuity equation implies that bodies travel in straight lines as the third section of this letter shows.

Anyone familiar with Newtonian mechanics or electromagnetism knows this is false. The continuity equation is underspecified and the field equations give the rest of the motion. For example, in electromagnetism we have $$\partial_\mu J^{\mu} = 0$$ for a current. In this we have one equation and four unknowns with Maxwell's equations providing the rest of the specification of the current. In the continuity equation for GR, there are four equations and ten unknowns and straight line motion is only one of infinite solutions.

I think it's a good illustration of the kinds of basic mistakes that people can make and that just because something is published in a journal does not mean it can be trusted.

 

[Vanadium 50]

I think it's a good letter.

It's wrong, but at least it's clear why it's wrong. As you point out, the author incorrectly calculates that bodies do not accelerate in gravitational fields (!), and then goes on to show (correctly, given the faulty premise) that there is no radiation in this situation. "Wrong but clear" is far more useful than what many people with unorthodox theories write - that's "wrong and inpenetrable"

 

[cellotim]

I think it's a good letter.

It's wrong, but at least it's clear why it's wrong. As you point out, the author incorrectly calculates that bodies do not accelerate in gravitational fields (!), and then goes on to show (correctly, given the faulty premise) that there is no radiation in this situation. "Wrong but clear" is far more useful than what many people with unorthodox theories write - that's "wrong and inpenetrable"

Yes, I agree. I think it's a good example of a basic mistake and one that's easy to make given the way the geodesic equation is set up. It's a good discussion point for logical fallacies. In this case, it's a classic fallacy of reversed implication, i.e. since constant velocity implies $$\partial_\mu T^{\mu\nu} = 0$$, the author assumes the converse. It would be less fatal if it weren't the entire purpose of the letter :). Otherwise, the author has a good understanding of how the quadrupolar formula is calculated in the Epstein-Wagoner formalism.

 

[Stingray]

I think that the author is claiming to consider two point particles (without "internal structure"). This makes no sense in full GR, but it is perfectly compatible with $\partial_\mu T^{\mu\nu}=0$. Plugging in the relevant form for the stress-energy tensor, it is easily shown that such particles must move on straight lines.

I think that he is implicitly bringing up a well-known source of confusion in GR: If treated as "exact," the linearized Einstein equations have no solutions unless $\partial_\mu T^{\mu\nu}=0$. But this is only true if the matter does not interact gravitationally. This is not a "theory of gravity" in any reasonable sense. There are ways out of this, but they require considerable care in the choice of approximations. Perturbation theory is tricky in GR, and many issues remain unclear even today.

 

[cellotim]

I think that the author is claiming to consider two point particles (without "internal structure"). This makes no sense in full GR, but it is perfectly compatible with $\partial_\mu T^{\mu\nu}=0$. Plugging in the relevant form for the stress-energy tensor, it is easily shown that such particles must move on straight lines.

I think that he is implicitly bringing up a well-known source of confusion in GR: If treated as "exact," the linearized Einstein equations have no solutions unless $\partial_\mu T^{\mu\nu}=0$. But this is only true if the matter does not interact gravitationally. This is not a "theory of gravity" in any reasonable sense. There are ways out of this, but they require considerable care in the choice of approximations. Perturbation theory is tricky in GR, and many issues remain unclear even today.

Yes, I see now. There is a difference. The continuity equation for electromagnetism is, $$\nabla\cdot\vec{J} + \partial \rho/\partial t = 0$$ or $$\partial_\mu J^{\mu} = 0$$ where $$J^{\mu} = (-\rho,\vec{v})$$ is underspecified. But the equation $$\partial_{\mu} T^{\mu\nu} = 0$$ has four equations, not enough to specify the ten components of the tensor but enough to specify the four velocity. Interesting. So, the author is making a different mistake than I thought.