🚀 go-pugleaf

In article <C1CGs3.Jqn@well.sf.ca.us> metares@well.sf.ca.us (Tom Van Flandern) writes:

>Since our
>last discussion I've learned of "Conservation of vector-valued forms and
>the question of the existence of gravitational energy-momentum in general
>relativity" by J.G. Vargas and D.G. Torr, Gen.Rel.&Grav. 23, 713-732
>(1991).  They conclude that the theory has some real problems, not just
>unaesthetic inconveniences from the geometrization of the physics.

>     Also "Nonexistence of multiple black holes in asymptotically Euclidean
>static vacuum space-time" by G.L. Bunting and A.K.M. Masood-ul-Alam,
>Gen.Rel.&Grav. 19, 147-154 (1987), argues for the conclusion in their
>title.  This paper also cites mathematical problems with GR, similar to
>those Yu, Vargas, and Tor pointed out.

But Tom, neither of these papers is relevant to the question of 
gravitational radiation in GR, though the first has some slightly
related comments.  In reverse order: the key word in the paper by
Bunting and Masood-ul-Alam is *static.*  Their argument demonstrates
that if you start with two (or more) neutral black holes at rest,
they won't remain at rest.  This is one of the nice features of GR
--- the field equations themselves determine the equations of motion.
There are, of course, exact solutions for static multiple *charged*
black hole configurations, in which gravitational attraction is
balanced by electrical repulsion (the so-called "electrovac"
solutions).  The only relevance I can see to gravitational radiation
is that a generalization of this paper might be able to prove the
*existence* of radiation in GR --- if the result can be extended from
static to stationary solutions, it could demonstrate that the orbits
of a pair of black holes must decay.

The Vargas and Torr article come slightly closer to supporting your
argument, but not by much.  They start by reformulating the standard
GR stress-energy conservation law as an integral conservation law in
a manner that requires no gravitational stress-energy pseudotensor.
(I haven't looked at this closely enough to decide whether I believe
it; for any experts out there, they essentially use a tetrad to
change one of the indices of T to a Lorentz index, but I'm not sure
whether they treat the spin connection term correctly.)  Then in
discussing their result, they say, "Let us suppose that the absence
of a gravitational source [of energy] is indeed a real problem in
general relativity, as it certainly is in the case of nongeometric
theories," and propose instead a version of teleparallel theory.

But they give virtually no reason to suppose that the absence of a
gravitational stress-energy tensor is a problem; in fact, general 
relativity gets along fine without one.  Their one argument seems
to be based on a misinterpretation of the paper by Bunting and
Masood-ul-Alam --- they seem to misunderstand the nonexistence of
static solutions to be the nonexistence of any solutions.  Apart
from that, the main lesson of this paper seems to be simply that
GR really isn't just Newtonian mechanics with some extra forces
thrown in, and that you shouldn't rely on Newtonian concepts like
energy as more than a heuristic guide.  Let me emphasize that *this
does not affect the analysis of gravitational radiation in GR* ---
while elementary textbooks may treat radiation in terms of energy
balance, the serious calculations in the field do not.  

>     I have now also seen another recent publication by Damour and Taylor
>containing their clearest statement yet that the binary pulsar does not
>prove the existence of gravity waves.  The source is: Phys.Rev.D 45, 
>1840-1868 (1992) [...]

Specifically, they discuss a set of models involving both a standard
GR term in the action and two long-range scalar fields, and show
that the parameters can be adjusted in such a way as to agree with
existing observations.  They *don't* say that these models exhibit
no gravitational radiation, by the way (I'm pretty sure they do; I'll
try to look up the paper by Damour and Esposito-Farese if it's
published yet); the amount of radiation is different, though, because
strong-field interactions are also different.

Is this surprising?  No experiment can "prove" that the predictions
of gravitational radiation in GR are correct; no matter how closely
the observations agree with predictions, one can always cook up a
theory with enough extra interactions and enough new parameters to
also agree.  The main purpose of the paper you cite is to
provide a general parametrization of possible models in order to
pin down what is and is not ruled out by a given observation.  
But it also concludes that so far, the existing standard theory
is in extremely good agreement with observation.  

If your point is simply that general relativity shouldn't be taken to
be the ultimate answer, I have no quarrel with you.  As an occasional
string theorist, I'm inclined to agree. But it's also important to
keep some perspective.  General relativity works, and it works very 
well; nothing in the Damour and Taylor article suggests otherwise.

Steve Carlip
carlip@dirac.ucdavis.edu