  We perform simulations of general relativistic rotating stellar core collapse
and compute the gravitational waves (GWs) emitted in the core bounce phase of
three representative models via multiple techniques. The simplest technique,
the quadrupole formula (QF), estimates the GW content in the spacetime from the
mass quadrupole tensor. It is strictly valid only in the weak-field and
slow-motion approximation. For the first time, we apply GW extraction methods
in core collapse that are fully curvature-based and valid for strongly
radiating and highly relativistic sources. We employ three extraction methods
computing (i) the Newman-Penrose (NP) scalar Psi_4, (ii)
Regge-Wheeler-Zerilli-Moncrief (RWZM) master functions, and (iii)
Cauchy-Characteristic Extraction (CCE) allowing for the extraction of GWs at
future null infinity, where the spacetime is asymptotically flat and the GW
content is unambiguously defined. The latter technique is the only one not
suffering from residual gauge and finite-radius effects. All curvature-based
methods suffer from strong non-linear drifts. We employ the fixed-frequency
integration technique as a high-pass waveform filter. Using the CCE results as
a benchmark, we find that finite-radius NP extraction yields results that agree
nearly perfectly in phase, but differ in amplitude by ~1-7% at core bounce,
depending on the model. RWZM waveforms, while in general agreeing in phase,
contain spurious high-frequency noise of comparable amplitudes to those of the
relatively weak GWs emitted in core collapse. We also find remarkably good
agreement of the waveforms obtained from the QF with those obtained from CCE.
They agree very well in phase but systematically underpredict peak amplitudes
by ~5-11% which is comparable to the NP results and is within the uncertainties
associated with core collapse physics. (abridged)
