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Assume that there are only well behaved functions as mass distributions, and there are no other forces except gravitation. Is it than possible to create an arrangement where a variation of a certain quantity (could be mass density or gravitational field or momentum) has a resonance?

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What do you mean by "variation"? And also, what do you mean by "resonance structure" exactly? I'm not sure whether you're talking about the same thing that physicists mean when they say "resonance." – David Z Nov 21 '10 at 3:28
@David Zaslavsky: i mean a variation in time or space. By resonance i mean an exponentially damped sinusoid . – Rajesh Dachiraju Nov 21 '10 at 3:32
So you're asking whether it's possible, using only gravitational forces, to create a situation in which some physical quantity $q$ has values given by an exponentially damped sinusoidal function of time, $q(t) \sim e^{-t/\tau}\cos(\omega t)$? If so, it seems like an odd question to ask. (In any case, "resonance structure" is almost certainly the wrong term to use here) – David Z Nov 21 '10 at 3:42
@David Zaslavsky: edited. – Rajesh Dachiraju Nov 21 '10 at 3:53
"Resonance in a gravitational field" makes me thing about that: . But your question is strangely stated.. – Cedric H. Nov 21 '10 at 11:04
up vote 2 down vote accepted

A matter distribution with a sinsuoidally varying monopole or dipole moment will only produce variations in the gravitational field within the matter distribution. If the quadrupole (or a higher multipole moment) varies sinsuoidally, you will produce gravitational waves in a way very analogous to how electromagnetic waves are produced, with the amplitude differing by just a few numeric constants.

I wouldn't expect the back-reaction of the wave to amplify the variation that created the wave in the first place, though. Is this what you mean by 'a resonance'?

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@Jerry Schirmer: what do you mean by a monopole and a dipole ? – Rajesh Dachiraju Nov 21 '10 at 5:21
Monopole moment: $M=\int d^{3}x\left(\rho\right)$. Dipole moment: $P^{i}=\int d^{3}x\left( x^{i}\rho\right)$. Quadrupole moment: $Q^{ij}=\int d^{3}x\left( x^{i}x^{j}\rho\right)$. There are further modifications that one can make if you are looking to make equations simpler (namely, subtracting traces of the quadrupole moment from itself), but that's the basic idea. – Jerry Schirmer Nov 21 '10 at 5:28
@Jerry Schirmer: please explain me in english without any notations – Rajesh Dachiraju Nov 21 '10 at 5:32
the monopole moment is the total amount of mass. The dipole moment is the amount of mass current flow. The quadrupole moment is more complicated, but is related to the moment of inertia from an intro physics course. But these things are best described with equations. – Jerry Schirmer Nov 21 '10 at 5:36
@Jerry Schirmer: do you mean dipole moment is momentum ? – Rajesh Dachiraju Nov 21 '10 at 5:44

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