# From the point of view of a moving source of light, is the wavefront always a sphere with them at the center?

Most diagrams regarding relativistic doppler effect always show in terms of an outside observer that is looking at both the light and the moving source. In this context, yes, the source moves towards the observer too so the observer does not see the source at the center of a sphere. The wavefront is still a sphere of course, just one with concentric spheres with different centers.

Now, let's remove this other obsever and just consider the source. No matter how fast the source moves, he always sees light moving at $$c$$. Not only that, but if we say that there is nothing else except for the source and the light that is being emitted, the source should just see himself as completely stationary. Therefore the observation should simply be that they are in the center of a sphere of light that has different frequencies. Is this correct?

EDIT: Now that I think about it, if we remove the other observer and anything else to use as a reference, it does not make sense to think of the source as having a velocity. So the situation is exactly the same as if the source was stationary - is this correct?