Derivation of the quadrupole moment of gravitational wave

AI Thread Summary
The discussion focuses on the derivation of the quadrupole moment of gravitational waves in the transverse traceless (TT) gauge. A participant suggests that standard general relativity texts typically cover this derivation, emphasizing that the provided equation represents the reduced quadrupole moment. It is clarified that this form is the trace-free part of the quadrupole moment. For those without access to such texts, a specific online resource is recommended for further information. Understanding the quadrupole moment is essential for studying gravitational waves.
Shan K
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Hi,
Can anyone give a derivation of the quadrupole moment in the TT gauge ( Equation metioned below ) of the gravitational wave ?

QijTT(x) = ∫ρ(xixj-1/3δijr2)d3x
Where ρ is the matter density

Thanks In Advance
 
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Hi Shan K. Do you own any general relativity texts? The TT gauge quadrupole moment is derived in almost every standard general relativity text. What you have written down is the reduced quadrupole moment and is simply the trace-free part of the quadrupole moment. If you don't own a general relativity text then check this out: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll6.html
 

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