What Are the Absorption Peaks of Gravitational Radiation Passing Through Earth?

[pervect]

I'm afraid I don't know the answer to these questions, but I thought they were interesting. (The topic came up in a different thread, I thought I'd start a new thead rather than hijack the old).

Suppose we have a 1 watt/m^2 beam of gravitaitonal radiation.

1) Where would be the first (lowest frequency) "absorption peak" of this radiation if it passed through the Earth? (I'm guessing that it would be where 1 wavelength = radius or diameter of th Earth)

2) How much power would the Earth absorb from such a beam? (This may depend on polarization, we are ideally looking for the "best match" to get optimum power transfer, but anything that is easy to calculate will do if it's the right order of magnitude).

3) Is the question properly posed so that it has an answer? (Is there any problem with defining the energy content of gravitational radiation as x joules/m^3 using pseudotensors, for instance - or is there a problem converting joules/m^3 to watts/m^2 - or is there any other conceptual problem with the question?).

 

[pervect]

Well, I'm close to being able to answer my own question after some reading.

I'm way off on the frequency - what's important is the mechanical resonat frequency of the Earth, which is, according to MTW pg 1036, about 54 minutes.

MTW gives some numerical information on the "cross section" of the Earth for randomly polarized gravity waves on the same page, but I'll have to read a bit before I understand what they are talking about.

 

[rbj]

Well, I'm close to being able to answer my own question after some reading.

i'm glad you did because i knew i couldn't help you. i don't know how to do tensors so i am pretty handicapped to do any real GR. i sort of understand GEM (gravitoelectromagnetism) and how to deal with gravitational radiation in that context, just like you would with Maxwell's Equations.

dunno how i would derive the resonant frequency of the Earth nor how to model it as some sort of resonator for gravity waves. i might be able to think out how to derive power intensity of gravitational radiation in the context of GEM, but it might not be right.

 

[pervect]

To do a good job of finding the resonant frequency of the Earth is apparently rather difficult. Using the Earth as a gravity wave detector is a proposal that has been already studied, so the problem has been addressed by some papers, cited in the textbook (MTW's Gravitation).