  Stars on orbits with pericenters sufficiently close to the supermassive black
hole at the center of their host galaxy can be ripped apart by tidal stresses.
Some of the resulting stellar debris becomes more tightly bound to the hole and
can potentially produce an observable flare called a tidal-disruption event
(TDE). We provide a self-consistent, unified treatment of TDEs by non-spinning
(Schwarzschild) black holes, investigating several effects of general
relativity including changes to the boundary in phase space that defines the
loss-cone orbits on which stars are tidally disrupted or captured. TDE rates
decrease rapidly at large black-hole masses due to direct stellar capture, but
this effect is slightly countered by the widening of the loss cone due to the
stronger tidal fields in general relativity. We provide a new mapping procedure
that translates between Newtonian gravity and general relativity, allowing us
to better compare predictions in both gravitational theories. Partial tidal
disruptions in relativity will strip more material from the star and produce
more tightly bound debris than in Newtonian gravity for a stellar orbit with
the same angular momentum. However, for deep encounters leading to full
disruption in both theories, the stronger tidal forces in relativity imply that
the star is disrupted further from the black hole and that the debris is
therefore less tightly bound, leading to a smaller peak fallback accretion
rate. We also examine the capture of tidal debris by the horizon and the
relativistic pericenter precession of tidal debris, finding that black holes of
$10^6$ solar masses and above generate tidal debris precessing by $10^\circ$ or
more per orbit.
