  The Energetic X-ray Timing Survey Telescope (EXIST) mission concept is under
study as the Black Hole Finder Probe (BHFP), one of the three Einstein Probe
missions in the Beyond Einstein Program in the current NASA Strategic Plan.
EXIST would conduct an all-sky imaging hard X-ray ($\sim$10-600 keV) survey
with unprecedented sensitivity: about 5 $\times 10^{-13}$ cgs over any factor
of 2 bandwidth, or comparable to that achieved at soft X-rays in the ROSAT
survey. The proposed angular resolution of 5arcmin, temporal resolution of
10microsec, energy resolution of 1-4 keV over the broad band, and duty cycle of
0.2-0.5 for continuous coverage of any source provide an unprecedented phase
space for timing and spectral studies of black holes --from stellar to
supermassive, as well as neutron stars and accreting white dwarfs. The large
sky coverage allows intrinsically rare events to be studied. One particularly
exciting example is the possible detection of tidal disruption of stars near
quiescent AGN. Super flares from SGRs could be detected out to the Virgo
cluster. The large duty cycle and all sky monitor nature of the mission will
enable QPOs from luminous AGN and BH X-ray binaries to be studied on timescales
not possible before. I provide an overview of the mission concept and Reference
Design, the X-ray timing science prospects for EXIST, and how these might be
further optimized in the current Study for EXIST as the BHFP so that EXIST
might include many of the desirable features of a next-generation timing
mission.
