🚀 go-pugleaf

In article <1993Jan7.085151.13461@nuscc.nus.sg> scip2124@nusunix1.nus.sg (MARC PAUL JOREF VAN LOO) writes:

>  There exists no decent derivation of the
>  gravitational radiation of a binary pulsar.
>  Yu's objection to this derivation is correct.
>  But I found out recently that it is not new:
>  Read the 16th lecture of Buchwald's book
>  17 simple lectures on GR. (1982).

Lecture 15, probably.  Buchdahl argues --- rather convincingly, I
think --- that the linear approximation "at best...might be taken
as a heuristic guide," for several reasons:
(1) it treats the motion of the sources inconsistently (the paths are
approximated as Keplerian, while actually they should be independent
straight lines at this order of approximation);
(2) fields are strong inside the sources, so the linear approximation
is not valid everywhere;
(3) it has not been shown that the linear approximation is the first
term in a convergent series, and, if so, what the characteristics of
the full series are; and
(4) it has not been shown that higher order corrections are small.
He calls for a mathematically sound rederivation of the radiation
formula ("which abandons any appeal to naive linearization on the one
hand and to energy complexes on the other and which, in fact, avoids
any redundant reference to `radiation' altogether").  He then adds
that some recent (as of 1981) work has made progress in this
direction.

These strike me as fair criticisms, although there will always be
argument about exactly how mathematically rigorous a result must be
before it is believable.  Remember, though, that considerable
progress has been made in the past eleven years.  

In particular, the "post-Minkowskian algorithm" of Damour and 
collaborators goes a considerable way towards meeting these 
objections: it provides a systematic expansion in which higher
order terms can be compared to lower order terms, and it treats
the motion of sources consistently.  Furthermore, Damour and
Schmidt have shown that this approximation is "reliable"  ---
that is, that it is at least locally an expansion of an exact
solution of the field equations  (see J. Math. Physics 31 (1990)
2441) --- and they have made some progress toward extending their
local results to global ones.

There is certainly work that remains to be done in this area.  In
particular, as I understand it, there are still difficulties in
giving a realistic treatment of compact sources.  There's no doubt
that there is still room for surprises; but my own guess is that
if you're looking for surprises in "established" physics, this
isn't your best bet.

(The journal with Yu's article is at the bindery, so I haven't
been able to read it yet; does it make an argument qualitatively
different from Buchdahl's?)

Steve Carlip
carlip@dirac.ucdavis.edu