gjphw@iham1.UUCP (07/20/84)
** I am tired of reading Stonehenge articles across 7 newsgroups! **
Now that I have your attention, I would like to make a suggestion that has
not received generous applause in the past. On two previous occasions, when
mentioning that Einstein's General Theory of Relativity does not permit grav-
ity waves (or gravitons), I received flames (most were polite though). Inev-
itably, someone misunderstood the original submission, so I would like to
expand. What this article refers to is the predictions of Einstein theory,
not any experimental facts about gravitational radiation.
A. Einstein published his relativity theory for accelerated reference frames
in 1916. At that time, Albert also explored the consequences of his new
theory. Since the nonlinearities made solutions extremely difficult to find,
and there did not appear any local tests that might require the exact field
equations, Albert looked for solutions to his theory in the weak field approx-
imation. This is the basis for the linearized theory of general relativity
(called Einstein theory). Einstein did find wave phenomena (1918) as one
solution to these weak field equations (among other goodies).
Unfortunately, as pointed out in *Principles of Relativity Physics* by
Anderson (1967), a solution to a linearized equation may not be a rigorous
solution to the original equations. He cites the experience of people working
in fluid mechanics, with the Navier-Stokes equations, as the basis for this
caution. To be safe, all solutions must be tried in the full nonlinear Ein-
stein theory.
The prototype for radiation by massless particles is electromagnetic radia-
tion. Using Maxwell's equations (or, more precisely, quantum electrodynam-
ics), electromagnetic radiation can be shown to carry energy and momentum, and
this energy release is associated with some activity of the source. There are
conditions where the Maxwell equations are too difficult to solve exactly, but
the physical situation can be established and an observation made. An inabil-
ity to solve the nonlinear equations does not mean that radiation is not gen-
erated. Also, note that the electromagnetic radiation is different in both
the near field (close to the source) and far field (far from the source)
regions.
Anderson refers to an exact solution called plane-fronted waves. These are
waves traveling through space but are far from any source and do not carry
momentum. In fact, the only exact solutions for wave phenomena occur using
certain symmetry conditions or special metrics in free space.
Of the three modern texts on Einstein theory, I have access to two (Misner,
Thorne, and Wheeler (1973) is not in this building's library). In Adler,
Bazin, and Schiffer (1975), gravity waves are treated in a section exercising
the use of the linearized equations. Weinberg (1976) is the one that directly
attacks the issue in the chapter on gravitational radiation (no known solu-
tions to the full equations outside of the near field region), but continues
on with the topic by restricting himself to far from the source and assuming
that the appropriate gravitons are generated. K. Thorne is one of the most
often cited names in the study of gravitational radiation, but all of this
work has been based upon the linearized equations.
The most recent text in my brief literature search is *General Relativity -
An Einstein Centenary Survey* (1979) edited by Hawking and Israel. The intro-
duction to this volume gives a good summary of the efforts to explore Einstein
theory. The latest efforts have demonstrated the existence of something
called null surfaces (something like wave crests?) whose equivalent mass
decreases between the surfaces. Still, the existence and movement of these
null surfaces has not been associated with any properties of a source mass.
Another approach uses asymptotic (expansion) solutions, but these have not
been able to link radiation produced with changes in the source.
Are we lost in efforts to solve the full nonlinear Einstein equations for
gravitational radiation? Perhaps not forever, but it certainly is tough now.
Numerically, there has been one interesting solution.
In 1977, a paper by Smarr was published that explored a numerical solution
to the full field equations for the axisymmetric (head-on) collision of two
black holes. Based upon the experience with the weak field approximations,
you might expect a generous supply of gravitational radiation. Smarr's exper-
iment yielded little radiation escaping far from the collision (source). It
was hoped that a less restrictive case would be performed soon for comparison.
Has anyone any knowledge or references about later (after 1979) numerical
solutions to the full Einstein equations?
In defense of the existence of gravitational radiation, someone mentioned
that a binary pulsar has been discovered that emits gravitons. One of the
articles in the centenary survey book was a review of gravitational radiation.
The author mentioned that no solutions of gravitational waves had been found
from the full equations, but otherwise devoted the next 30 pages to a detailed
review of gravitational radiation. In 1976, a binary pulsar was discovered in
which the orbital elements of the binary system required the employment of
Einstein theory (the gravitational fields were considered to exceed those for
which Newton theory is appropriate). It would require about 10 years to
clearly establish the value of any orbital decay. The article goes on to
describe about 5 different mechanisms, gravitational radiation being one of
them, that could be used to account for the loss of orbital energy. Does any-
one know of other strong field binary systems?
In the next few years, several gravitational radiation detectors are
expected to begin operating. These second generation of devices are designed
to be about an order of magnitude (10) more sensitive than Weber's detector
(no one else has been able to confirm J. Weber's claims for detecting gravita-
tional radiation). The value in exploring a theory before experiments have
detected anything is that when, and if, something does turn up, it can quickly
be identified. If the linearized Einstein theory is used, space should be
overflowing with gravitational radiation. The nonlinear Einstein theory does
not appear to permit much radiation to escape into the far field region. What
will this next generation of detectors find?
--
Patrick Wyant
AT&T Bell Laboratories (Naperville, IL)
*!iham1!gjphw