From: carlip@landau.ucdavis.edu (Steve Carlip)
Newsgroups: sci.physics
Subject: Re: Has the Hulse-Taylor Pulsar GR "Observation" Been Retracted? (was Re: Beckmann Physics)
Date: 23 Dec 92 05:40:36 GMT
Followup-To: sci.astro
Organization: Physics, UC Davis

In article <BzD34p.Gpv@well.sf.ca.us> metares@well.sf.ca.us (Tom Van Flandern) writes:
>
>carlip@landau.ucdavis.edu (Steve Carlip) writes:
>
>> there is absolutely no doubt that general relativity predicts gravitational
>> radiation --- this can be shown through exact solutions, numerically, by
>> use of systematic approximation procedures, and by general arguments about
>> the asymptotic structure of spacetime.
>
>     "Absolutely no doubt"?  Then why is this point being contested by
>several GR specialists currently?  Take the 1992 Yu paper as the latest
>example.  Can you provide a clear, understandable refutation of his argument?
>(See my summary in a simultaneous reply to Matt Austern.)  If so, will you be
>publishing a rebuttal?  I'd realy like to get this point cleared up.
>

What we have here is a failure to communicate....

There are at least five issues I can think of that are getting mushed together
here, causing nearly infinite confusion.  They are:
1. Does general relativity predict gravitational radiation under any
circumstances?
2. Are certain specific systems (e.g., binary stars) predicted to radiate?
3. If so, how much should they radiate?
4. How can such radiation be observed in the measurable behavior of such
systems?
5. Are these predictions in agreement with actual observation?

The point I was addressing in the extract above was point 1.  There is
really no question that the field equations of general relativity admit
solutions describing gravitational radiation.  See, for instance, J.B. 
Griffiths' new book, _Colliding Plane Waves in General Relativity_
(Clardendon, 1991).  Or the book by Kramer et al., _Exact Solutions of
Einstein's Field Equations_ (Cambridge Univ. Press, 1980), especially
the sections "Colliding Plane Waves," "Closed Universes Built Up from
Gravitational Waves," and "Plane-fronted Gravitational Waves with Parallel
Rays."  Or, to pick a recent journal article at random, A. Wang, Int. J.
Mod. Phys. 6 (1991) 2273, which derives a five-parameter class of colliding
gravitational wave solutions of the field equations.  

You may object that most of the known exact solutions are physically
unrealistic, representing infinite plane or cylindrical waves.  But if
you look at Cutler and Wald, Class. Quantum Gravity 6 (1989) 453, you'll
find a mathematically rigorous proof of the existence of solutions of
the field equations of general relativity representing isolated systems
that lose mass by gravitational radiation.  Similar existence proofs
are discussed by Friedrich in the book _Recent Advances in General
Relativity_ (Janis and Porter, editors, Birkhauser, 1992).  Friedrich
also gives a nice summary of the use of asymptotic methods to carefully
define and quantify gravitational radiation.  

The other issues above are certainly less clear-cut, although in my opinion
the remaining questions are unlikely to turn out to give us any big
surprises.  For instance, there are certainly questions of mathematical 
rigor in the use of certain approximations used to derive the amount of 
radiation expected from a binary system, but my (limited) understanding 
is that most of these are close to resolution.  I've been told of a proof 
that Damour's "post-Minkowskian expansion" is asymptotic to an exact solution, 
for instance, but I don't have the reference with me.  There are likely to
be some small surprises --- such as Christadoulou's observation of a
"memory effect" of gravitational radiation (Phys. Rev. Lett. 67 (1992) 1486)
--- but there are so many different approaches converging on the same
general answer that it would be quite startling to find that they were all
wrong.

I'm on vacation at the moment, and the library here doesn't have Yu's
article.  I'll be glad to look at it when I get back to Davis.  Based
on your brief summary, though, I must say that I am quite skeptical.  

In particular, you discuss the problem of finding a local definition of
mass or energy density in general relativity.  This is a red herring
--- this issue was thrashed out in the early '60's.  It is certainly 
correct that it is difficult to define a local energy density, though
Penrose's "quasi-local mass" is a possible idea (see Tod, Class. Quantum
Gravity 7 (1990) 2237 for an application to gravitational radiation.)
However, there is an unambiguous definition of total energy in any spacetime
with suitable asymptotic behavior, the Bondi mass (Bondi et al, Proc.
Roy. Soc. 269 (1962) 21), which is measured at null infinity ("retarded
time") and which decreases monotonically when gravitational radiation
occurs.  There is also a standard measure of the flux of radiation at
infinity, essentially Bondi's "news function," which is also unambiguous
given suitable asymptotic behavior of spacetime.  I don't wish to claim that
the field is closed --- as I understand it, there are interesting open
questions about how to join rigorous results about asymptotic behavior
to approximate results about the smaller distance behavior of particular
sources --- but things really aren't nearly as vague as you suggest.

More in early January, if I can find Yu's paper.... Or if there's anyone
out there who actually works on gravitational radiation, I'll be glad to
bow out (I mostly do quantum gravity, such as it is, myself).

Steve Carlip
carlip@dirac.ucdavis.edu
Newsgroups: sci.physics