From: steinly@topaz.ucsc.edu (Steinn Sigurdsson)
Newsgroups: sci.astro
Subject: Re: The Hole Story
Date: 23 Dec 92 09:30:54
Organization: Lick Observatory/UCO
NNTP-Posting-Host: topaz.ucsc.edu
In-reply-to: Leigh Palmer's message of Wed, 23 Dec 1992 05:15:29 GMT

In article <1992Dec23.051529.16459@sfu.ca> Leigh Palmer <palmer@sfu.ca> writes:

   In article <STEINLY.92Dec22104345@topaz.ucsc.edu> Steinn Sigurdsson, 
   steinly@topaz.ucsc.edu writes:
   >In article <1992Dec22.011638.21749@sfu.ca> Leigh Palmer <palmer@sfu.ca> 
   writes:

   >   In article <STEINLY.92Dec20193619@topaz.ucsc.edu> Steinn Sigurdsson, 
   >   steinly@topaz.ucsc.edu writes:

   >   >I suppose I should read the paper, but there are exact solution of
   >   >plane gravitational waves for GR. They're literal solution of the
   >   >Einstein equation.

   >   That's interesting. Are gravitational plane waves susceptible to 
   >   (linear) Fourier decomposition? Do they comprise a spanning set for 
   >   all gravitational wave solutions? If they are not superposable, how 
   >   would one generate a gravitational plane wave?

   >Gravitational waves are not in general superposable because they
   >couple to each other - they carry stress-energy. All the exact
   >solutions I know of are ones with special symmetry in vacua, although
   >I only have a passing familiarity with the subject.

   That being the case, one cannot infer from the existence of plane wave 
   solutions that waves generated by, for example, a binary compact sytem, 
   will exist which are solutions of GR. In electrodynamics the existence of 

True. The gravitational radiation posited for the binary pulsars is
derived by taking linearised perturbations of the metric and looking
for solutions propagating to infinity - the normal formalism due
to Hartle chooses a particularly nice gauge and considers asymptotic
states in the far (weak) field where mode coupling is (hopefully)
negligible. As Loren notes, you do have to allow for the radiation reaction.

   plane wave solutions implied the existence of many other sorts of 
   solutions by Fourier's Theorem, and it seems that a leap has been made of 
   a similar sort which is not justified in the case of GR.

   Thus we return to the question of whether a binary compact system can 
   radiate. It is not immediately obvious to me that it should radiate plane 
   waves (indeed that possibility is ruled out because plane waves are 
   infinite in extent). Does a radiative solution to GR exist which has a 
   symmetry more appropriate to the case of the binary pulsar?

I think there are exact solutions with cylindrical symmetry (in
vacuum), although I wouldn't swear to it.
BTW the usual solution you see for binary pulsars is an orbit averaged
solution (ie it is assumed dJ/dt << J/P_orb ) The shape of the wave
form as this approximation breaks down during final stages of
spiral-in are the subject of ongoing research.

   I'd also like to ask again my previous question: how would one generate a 
   gravitational plane wave? I have trouble wraping (or warping) my 

Take a quadrupole and shake it ;-)
Be sure to check out the gravitational wave generator in the
Theoretical AstroPhysics Interaction Room at Caltech (with
the appropriate gauge setting and tunable frequency) should
you happen to be in the vicinity sometime in the next 6-8 months...

*  Steinn Sigurdsson   			Lick Observatory      	*
*  steinly@lick.ucsc.edu		"standard disclaimer"  	*
*  The laws of gravity are very,very strict			*
*  And you're just bending them for your own benefit - B.B. 1988*

Newsgroups: sci.astro,sci.physics