Electromagnetic Field of an Oscillating Point Charge Measured by a Transversely Comoving Observer

Abstract: We investigate the electromagnetic field produced by a harmonically oscillating point charge and measured by a spatially separated observer undergoing the same motion. We evaluate the exact retarded field on the observer's worldline and project the electromagnetic field tensor onto the observer's local orthonormal tetrad. This construction yields the electric and magnetic fields, electromagnetic energy density, and Poynting vector measured as functions of the observer's proper time. Our formulation separates unambiguous local observables from the observer-dependent classification of a field as radiation and provides a concrete setting in which to examine how a charge that is spatially static in a non-inertial coordinate system can nevertheless produce time-dependent locally measured fields.