Maxwell Field of a Charge in Hyperbolic Motion

Abstract

We conduct a detailed study of the electromagnetic field produced by a massive point particle undergoing hyperbolic (uniformly accelerated) motion in Minkowski space-time. Starting from the Liénard–Wiechert solution and using a covariant notation, we obtain and analyse the main quantities that describe this field. We identify the space-time region to which this solution is restricted and write a solution valid in the whole of space-time. Finally, we verify that this solution satisfies Maxwell’s equations in the sense of distributions.

Keywords

• Liénard–Wiechert potential
• relativistic hyperbolic motion
• Maxwell equations
• tensor distributions