Re: Is LIGO just observing viscosity of the vacuum?

I wrote
[[about general-relativistic gravitational-radiation damping in orbiting
binary systems]]
A lot of work has been done on this in the past decade, and the
equations of motion for a compact binary system are now known up to
and including (v/c)^7 terms. ??(This is often called "3.5-post-Newtonian"
order.) ??The (v/c)^5 order gives the standard quadrupole formula;
higher orders give small corrections to the quadrupole formula.

Igor Khavkine
Interesting. Now, I wonder how this result meshes with the claim made
in Landau & Lifshits. What they do is derive an effective Lagrangian.
Now, a Lagrangian formulation necessarily neglects non-conservative
(radiation, friction) effects. From what you say, the equations of
motion which include terms up to (v/c)^7 will necessarily have
friction terms and thus cannot come from an effective Lagrangian. Is
that correct?

I _think_ that is true starting at (v/c)^5 (where the first "fraction"
terms appear). But I should add the caveat that I'm not an expert in
this type of calculation.

Let's see, a quick search through my collection of "interesting papers"
reveals a short review paper, gr-qc/0611142, "General Relativistic
Dynamics of Compact Binary Systems", by Luc Blanchet (who is one of the
world's best experts in this sort of calculation). This paper describes
equations of motion up through (v/c)^7 terms (often called
"3.5-post-Newtonian"). The abstract reads

The equations of motion of compact binary systems have been derived
in the post-Newtonian (PN) approximation of general relativity. The
current level of accuracy is 3.5PN order. The conservative part of
the equations of motion (neglecting the radiation reaction damping
terms) is deducible from a generalized Lagrangian in harmonic
coordinates, or equivalently from an ordinary Hamiltonian in ADM
coordinates. As an application we investigate the problem of the
dynamical stability of circular binary orbits against gravitational
perturbations up to the 3PN order. We find that there is no innermost
stable circular orbit or ISCO at the 3PN order for equal masses.

The article goes on to state that the conservative part is obtained
by neglecting the 2.5PN (i.e., (v/c)^5) and 3.5PN (i.e., (v/c)^7) terms.
So it looks like you (Igor) are right: once these terms are included
a simple point-particle Lagrangian doesn't suffice any more.

ciao,

--
-- "Jonathan Thornburg [remove -animal to reply]" <jthorn@xxxxxxxxxxxxxxxxxxxxxxx>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"If the triangles made a god, it would have three sides." -- Voltaire

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