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Non-radiation charge density

If we can agree to that according to Goedecke it is enough to prove that the fourier transform in time and space is zero for all waves associated with the speed of light we can use the following route …
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Non-radiation charge density

For all $l,m$ but $l=0,m=0$, can we find $r_0,w_0$ such that the following charge distributions can represent a charge field that does not radiate: $$ \rho(r,\theta,\phi) = \Re(c_{l,m} Y_{l,m}(\theta …
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