  We present results from the first 2D and 3D simulations of the collapse of
rotating stellar iron cores in general relativity employing a
finite-temperature equation of state and an approximate treatment of
deleptonization during collapse. We compare fully nonlinear and conformally
flat spacetime evolution methods and find that the conformally flat treatment
is sufficiently accurate for the core-collapse supernova problem. We focus on
the gravitational wave (GW) emission from rotating collapse, core bounce, and
early postbounce phases. Our results indicate that the GW signature of these
phases is much more generic than previously estimated. In addition, we track
the growth of a nonaxisymmetric instability of dominant m = 1 character in one
of our models that leads to prolonged narrow-band GW emission at ~930 Hz over
several tens of milliseconds.
