  Extrasolar circumbinary planets are so called because they orbit two stars
instead of just one; to date, an increasing number of such planets have been
discovered with a variety of techniques. If the orbital frequency of the
hosting stellar pair is much higher than the planetary one, the tight stellar
binary can be considered as a matter ring current generating its own
post-Newtonian stationary gravitomagnetic field through its orbital angular
momentum. It affects the orbital motion of a relatively distant planet with
Lense-Thirring-type precessional effects which, under certain circumstances,
may amount to a significant fraction of the static, gravitoelectric ones,
analogous to the well known Einstein perihelion precession of Mercury,
depending only on the masses of the system's bodies. Instead, when the
gravitomagnetic field is due solely to the spin of each of the central star(s),
the Lense-Thirring shifts are several orders of magnitude smaller than the
gravitoelectric ones. In view of the growing interest in the scientific
community about the detection of general relativistic effects in exoplanets,
the perspectives of finding new scenarios for testing such a further
manifestation of general relativity might be deemed worth of further
investigations.
