Aims: We investigate the electromagnetic interaction of a relativistic stellar wind with a planet or a smaller body in orbit around the star. This may be relevant to objects orbiting a pulsar that are expected to hold a planetary system, such as PSR B1257+12 and PSR B1620-26, or to pulsars with suspected asteroids or comets.
Methods: We extend the theory of Alfvén wings to relativistic winds.
Results: When the wind is relativistic but slower than the total Alfvén speed, a system of electric currents carried by a stationary Alfvénic structure is driven by the planet or by its surroundings.For an Earth-like planet around a "standard" second pulsar, the associated current can reach the same magnitude as the Goldreich-Julian current that powers the pulsar's magnetosphere.