  A large fraction of white dwarfs (WDs) may host planets in their habitable
zones. These planets may provide our best chance to detect bio-markers on a
transiting exoplanet, thanks to the diminished contrast ratio between the
Earth-sized WD and its Earth-sized planets. The JWST is capable of obtaining
the first spectroscopic measurements of such planets, yet there are no known
planets around WDs. Here we propose to take advantage of the unique capability
of the Kepler spacecraft in the 2-Wheels mode to perform a transit survey that
is capable of identifying the first planets in the habitable zone of a WD. We
propose to obtain Kepler time-series photometry of 10,000 WDs in the SDSS
imaging area to search for planets in the habitable zone. Thanks to the large
field of view of Kepler, for the first time in history, a large number of WDs
can be observed at the same time, which is essential for discovering transits.
Our proposed survey requires a total of 200 days of observing time, and will
find up to 100 planets in the WD habitable zone. This survey will maintain
Kepler's spirit of searching for habitable Earths, but near new hosts. With
few-day observations and minute-cadences per field, it will also open up a
completely unexplored discovery space. In addition to planets, this survey is
sensitive to pulsating WDs, as well as eclipsing short period stellar and
substellar companions. These have important implications for constraining the
double WD merger rate and their contribution to Type Ia supernovae and the
gravitational wave foreground. Given the relatively low number density of our
targets, this program can be combined with other projects that would benefit
from high cadence and many-fields observations with Kepler, e.g. a transit
survey of a magnitude-limited, complete sample of nearby M dwarfs or
asteroseismology of variable stars (e.g. RR Lyrae) in the same fields.
