  We investigate the evaporation of close-by pulsar companions, such as
planets, asteroids, and white dwarfs, by induction heating. Assuming that the
outflow energy is dominated by a Poynting flux (or pulsar wave) at the location
of the companions, we calculate their evaporation timescales, by applying the
Mie theory. Depending on the size of the companion compared to the incident
electromagnetic wavelength, the heating regime varies and can lead to a total
evaporation of the companion. In particular, we find that inductive heating is
mostly inefficient for small pulsar companions, although it is generally
considered the dominant process. Small objects like asteroids can survive
induction heating for $10^4\,$years at distances as small as $1\,R_\odot$ from
the neutron star. For degenerate companions, induction heating cannot lead to
evaporation and another source of heating (likely by kinetic energy of the
pulsar wind) has to be considered. It was recently proposed that bodies
orbiting pulsars are the cause of fast radio bursts; the present results
explain how those bodies can survive in the pulsar's highly energetic
environment.
