  The Class A stellar engine (also known as a Shkadov thruster) is a spherical
arc mirror, designed to use the impulse from a star's radiation pressure to
generate a thrust force, perturbing the star's motion. If this mirror obstructs
part of the stellar disc during the transit of an exoplanet, then this may be
detected by studying the shape of the transit light curve, presenting another
potential means by which the action of extraterrestrial intelligence (ETI) can
be discerned. We model the light curves produced by exoplanets transiting a
star which possesses a Shkadov thruster, and show how the parameters of the
planet and the properties of the thruster can be disentangled. provided that
radial velocity follow-up measurements are possible, and that other obscuring
phenomena typical to exoplanet transit curves (such as the presence of
starspots or intrinsic stellar noise) do not dominate. These difficulties
aside, we estimate the a priori probability of detecting a Shkadov thruster
during an exoplanet transit, which even given optimistic assumptions remains
stubbornly low. Despite this, many exoplanet transit surveys designed for
radial velocity follow-up are on the horizon, so we argue that this remains a
useful serendipitous SETI technique. At worst, this technique will place an
upper limit on the number of Class A stellar engines in the Solar
neighbourhood; at best, this could help identify unusual transiting exoplanet
systems as candidates for further investigation with other SETI methods.
