Does a free falling charge radiate ?

WannabeNewton

Yeah that would be cool. It is quite instructive to take a ring of test particles as your family of closely separated geodesics and see how the gravitational waves expand and shear them. There is a close relationship between the Weyl tensor as a contributor to shear and the Ricci tensor as a contributor to expansion, as codified by the Raychaudhuri equation (however they are coupled so it isn't exactly totally independent)