Completing the Lienard-Wiechert potentials: The origin of the delta function fields for a charged particle in hyperbolic motion

Calculating the electromagnetic fields of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. In particular, the fields calculated from the Liénard-Wiechert potentials fail to satisfy Maxwell\u27s equations. While the correct fields have been obtained many times and through various means, it has remained unclear why the standard approach fails. We identify and amend the faulty step in the Liénard-Wiechert construction and provide a new direct calculation of the fields and potentials for acharge in hyperbolic motion