NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/astro/14312

Internet Message Format | 1993-01-23 | 2.9 KB

Path: sparky!uunet!usc!sdd.hp.com!hplabs!ucbvax!ucdavis!landau.ucdavis.edu!carlip
From: [e-mail] (Steve Carlip)
Newsgroups: sci.astro
Subject: gravitational radiation one more time
Message-ID: <[e-mail]>
Date: 22 Jan 93 19:02:06 GMT
Sender: [e-mail]
Organization: Physics, UC Davis
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For all you gravitational radiation fans out there:

I finally got hold of the article by Yu that Tom van Flandern
cited last month as proof that there was still debate about
gravitational radiation in general relativity (Astrophysics and
Space Science 194 (1992) 159).  What a disappointment!  I was
hoping for an interesting argument, even though I expected it
to be wrong; instead, I found --- excuse a little rudeness ---
a paper that was basically silly.

Now that I've gotten that out of my system, here's the critique.
Yu's argument is as follows.  The standard quadrupole formula
for gravitational radiation in GR is calculated in the linear
approximation.  But in that approximation, the stress-energy
tensor is exactly conserved (its ordinary divergence is zero,
as opposed to its covariant divergence).  Therefore the energy
of a binary star system cannot change; therefore no energy can
be radiated away.

Yu adds a few bells and whistles (he introduces the gravitational
pseudotensor), but that's the essence of the paper.  Of course,
he could have gone further --- in this approximation, not only
don't binary stars lose energy, they don't orbit, moving instead
in straight lines.  Yu even derives this fact in equation (3.1),
but instead of saying, ``Hey, something's wrong here,'' he moves
on without comment.

The problem, of course, is simply that the particular approximation
Yu uses is inconsistent --- terms are thrown away that are as large
as those that are kept.  This is old, old news.  Misner, Thorne,
and Wheeler have a nice discussion of exactly this point on page
443.  They also have a great index entry: ``Linearized theory of
gravity, self-inconsistency of,'' with subentries ``partial repair
for slow-moving systems leads to Newtonian and post-Newtonian
formalisms'' and ``complete repair of, leads to general relativity.''

Sorry, but this is really kindergarten stuff --- of course you have
to be careful about consistency of approximations, but anyone who
works in the field knows this.  Indeed, most relativists view this
as a feature, not a bug; an old result of Deser's shows that by
adding the nonlinear terms needed to correct the inconsistency of
the linear approximation, you automatically bootstrap up to the
full Einstein equations.

Incidentally, I think Yu knows he's on shaky ground, since he says,
``Refinements of the Einstein linearized theory...are not discussed in
detail...as they have not yet entered standard GR textbooks to date,''
though he then mentions MTW, which does discuss these issues.

Steve Carlip
[e-mail]