claus (02/11/83)
Haswaves? Namely, do they exist, and if they do what are some of their properties. I'm interested in how fast the wave would propagate through space. An example of this would be when a star collaspes into a black hole, how long would it take before this could be detected at a certain distance. Any responses would be appreciated, Dave Claus ABI/Indy inuxa!claus
sharp@aquila.UUCP (09/10/84)
An earlier article stated that "Einstein's General Theory of Relativity
does not permit gravity waves (or gravitons)". This is a particularly
strong statement, and I'm sure that the author did not mean to be quite
so dogmatic. The argument that followed was based on the assertion that
the only known solutions for gravitational radiation are solutions of the
linearized equations of GR, and, as is well known, solutions to approximate
equations may not approximate solutions of the full equations. I intend
here to address this question, correct a few misconceptions apparent from
various queries and arguments, and try to present the current conventional
point of view. All discussions will be welcome.
Existing approaches:
The original discussion of gravitational radiation was by Einstein in 1918
(Preuss.Akad.Wiss.Berlin Sitzber. 1918, 154). He made some serious
restrictive assumptions: 1) the internal motions of the source are governed
by non-gravitational forces (this is called the "negligible self-gravity"
assumption), 2) these forces are small compared to the mass-energy density
("weak stress"), 3) the source is small compared to the characteristic
wavelength of the radiation it emits (since this implies internal velocities
small compared to that of light, it is known as the "slow motion" approx.).
It has subsequently been shown that the negligible self-gravity assumption
is not necessary (perhaps as early as Landau & Lifshitz, 1941, The Classical
Theory of Fields (translations have later dates)), and later that the
weak stress assumption can also be dropped (Thorne, 1980, Rev.Mod.Phys vol 52).
The Thorne article brings together in a review all of the slow motion ideas
and methods, which are based on a multipole expansion of the radiation
field. The conservations of mass and of momentum imply that the lowest order
term in such an expansion is quadrupole, which is therefore the type of
radiation most discussed (note that other, non-GR, theories may have dipole
radiation, but I'm currently sticking to GR).
NOTE: none of this work insists on weak fields. However, strong fields usually
imply fast motions, and most astrophysically interesting possible sources
will also have fast motions, so that other approaches have since been developed.
First, there are weak gravity formalisms, which DO use either linearized
gravity or a small modification known as post-linear theory (Thorne, 1977, in
Topics in Theoretical and Experimental Gravitation Physics, eds V. de Sabbata
and J. Weber [side-note: this was a conference called by Weber after some
years of pioneering the search for gravity waves, which turned out to set
the direction of research for all subsequent work])
Second, there are the very high speed formalisms, principally developed by
D'Eath (see his article in the very valuable conference proceedings edited
by Larry Smarr, called Sources of Gravitational Radiation, pub. 1979 by CUP)
These methods do not require weak gravity, and have been used for things such
as the head-on collision of fast-moving black holes.
Next, there are perturbation methods, which consider weak perturbations of
non-radiating systems. Examples are small objects falling into black holes,
or small asymmetries during the collapse to a black hole. I know of no
particularly good review, since this is a rapidly developing field, but the
Smarr volume contains several representative articles.
Finally, there are the methods which actually solve the full, non-linear
equations of GR, with none of the above assumptions. These are all numerical
methods, involving computer solutions. It took a long time for these
approaches to get underway, for technical reasons, but finally work by Smarr
and by Epley (who managed to solve the question of just exactly what is
radiation in a non-linear, strong field, dynamically evolving system),
inspired by Bryce DeWitt and drawing strongly on the expertise of Jim Wilson,
has left us in the position to calculate the evolution of realistic,
astrophysically interesting configurations. As you can imagine, this is a
very rapidly growing field, occasionally slowed down when its protagonists
go off and get real jobs. Work is being done all over the world. At the
moment, all published material is based on various symmetry assumptions,
because that way you only have to deal with one or two spatial dimensions
along with the time dimension. The full, 3-space, 1-time, problems are
now being tackled, but that's where you really ought to have a Cray.
Now, the basic results of all this work are to confirm and support each other.
The equations DO allow for radiation, and the different approaches seem to
agree (where they overlap). The principal technical argument of which I am
aware is an objection to the calculations of radiation reaction (i.e. the
effect on the source) and to the conservation laws predicting the source's
loss of energy and momentum (linear and angular). These objections are
slowly fading with more rigorous mathematical work, and different approaches.
[Now, an aside about quantisation and gravitons: the wave equations derived
from GR are those appropriate for particles of zero rest mass and spin two.
In this sense, we can consider GR as a non-linear field theory, mediated
by the exchange of virtual gravitons. No fully successful quantisation
of this field theory exists (i.e. no "second quantisation", no quantum gravity),
although there's a lot of work going on ! However, for the physics of
radiation this is irrelevant, because gravitational waves are emitted
by the bulk motions of huge amounts of matter, so that the occupation
numbers of the gravitons' QM states are enormous - around 10**75. Since the
QM corrections have fractional magnitude ~ SQRT(N), we can forget them.]
Having said all of this in defense of theory, a word or two about practice.
Ultimately, the only resolution of the argument will be the detection of
gravitational waves, or putting such stringent limits on the lack of
detection that no theoretical "fudging" will be able to cope.
At the moment, there are no reliable detections of gravity waves in the
laboratory (see also an article in Science News for Aug 4th), but the
current generation of detectors will either see something or cause serious
theoretical upheaval. The (in?)famous binary pulsar is often quoted as
supporting the formulae for energy loss, because the observed decay is
close to (slightly above) the predicted value. However, there are other
possible energy loss mechanisms, so work on that object continues.
(Incidentally, it should be noted that had the observations found an
energy loss LESS than that predicted by gravitational radiation, we would
already have known that the theory was wrong.) Basically, there is more
than enough confidence in the theory to continue the experimental searches.
In case anyone is worried about all this useless research, there was a
review conducted for the NSF by a group of scientists not working in the
field (Deslattes, Edwards, Jacobs, Nygren, Rich, and Wilkinson, April 22,
1979, report from the Technical Review Subcommittee), which says, in part,
"The rate of progress in the recent past has been excellent, both in terms
of increased instrumental sensitivity and generally useful high-technology
spinoffs.....The ultimate detection of gravitational waves, verification of
the properties predicted by theory, and exploitation for observational
astronomy, are believable consequences of present research directions."
These are the most sensitive experiments in progress, reaching down to the
quantum Heisenberg uncertainty limit, and even beyond (very clever stuff).
As remarked by one of the experimenters, you have to remember that the sort
of motions they're trying to measure are equivalent to a millimeter over
a baseline of an astronomical unit.
Enough for now. Any comments or further questions ?
--
Nigel Sharp [noao!sharp National Optical Astronomy Observatories]