On the paper by John Wheeler that first introduced the concept of "geons", he states that when one tries to construct such geons with spherical symmetry, incoherence of the different EM modes is essential since
If all [disturbances] had the same frequency, they would add incoherently to form a single mode of electromagnetic field strenght. But there is no such thing as a nonzero source-free spherically symmetrical electromagnetic field disturbance.
Why is it that there cannot be a "a nonzero source-free spherically symmetrical electromagnetic field disturbance"? Where does this result comes from?
