  We report on a remarkable class of exact solutions to force-free
electrodynamics that has four-current along the light cones of an arbitrary
timelike worldline in flat spacetime. No symmetry is assumed, and the solutions
are given in terms of a free function of three variables. The field
configuration should describe the outer magnetosphere of a pulsar moving on the
worldline. The power radiated is the sum of an acceleration (Larmor-type) term
and a pulsar-type term.
