Gravitational Waves: Why They're Produced & Detection

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Hi, I have been reading about gravitational waves for the last few days. I saw any cylindrically or spherically symmetric body can not produce gravitational wave, can you please explain to me why ?

I also need a brief explanation on why GW are actually produced.

regards
 
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In order to produce gravitational waves the source distribution must have a non-vanishing quadrupole moment that has a non-zero third time derivative. A spherical distribution for example has identically vanishing quadrupole moment in and of itself. However if you have the spherical distribution spin about a fixed axis then you will have a non-vanishing quadrupole moment and gravitational waves can be generated. This is all in the wave-zone approximation. In EM we also make the wave-zone approximation and in this case EM waves are generated from second time derivatives of dipole moments of charge distributions so you can compare this with the case of gravitational waves.
 
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