Kepler's first major discoveries are two hot (T > 10,000 K) small-radius objects orbiting stars in its field. A viable hypothesis is that these are the cores of stars that have each been eroded or disrupted by a companion star. The companion, which is the star monitored today, is likely to have gained mass from its now-defunct partner and can be considered to be a blue straggler. KOI-81 is almost certainly the product of stable mass transfer; KOI-74 may be as well, or it may be the first clear example of a blue straggler created through three-body interactions. We show that mass-transfer binaries are common enough that Kepler should discover ~1000 white dwarfs orbiting main-sequence stars. Most of these, like KOI-74 and KOI-81, will be discovered through transits, but many will be discovered through a combination of gravitational lensing and transits, while lensing will dominate for a subset. In fact, some events caused by white dwarfs will have the appearance of "anti-transits"—i.e., short-lived enhancements in the amount of light received from the monitored star. Lensing and other mass-measurement methods provide a way to distinguish white dwarf binaries from planetary systems. This is important for the success of Kepler's primary mission, in light of the fact that white dwarf radii are similar to the radii of terrestrial planets, and that some white dwarfs will have orbital periods that place them in the habitable zones of their stellar companions. By identifying transiting and/or lensing white dwarfs, Kepler will conduct pioneering studies of white dwarfs and of the end states of mass transfer. It may also identify orbiting neutron stars or black holes. The calculations inspired by the discovery of KOI-74 and KOI-81 have implications for ground-based wide-field surveys as well as for future space-based surveys.
