  Long-duration gamma-ray bursts (lGRBs) originate in relativistic collimated
outflows -- jets -- that drill their way out of collapsing massive stars.
Accurately modeling this process requires realistic stellar profiles for the
jets to propagate through and break out of. Most previous studies have used
simple power laws or pre-collapse models for massive stars. However, the
relevant stellar profile for lGRB models is in fact that of a star after its
core has collapsed to form a compact object. To self-consistently compute such
a stellar profile, we use the open-source code GR1D to simulate the
core-collapse process for a suite of low-metallicity, rotating, massive stellar
progenitors that have undergone chemically homogeneous evolution. Our models
span a range of zero-age main sequence (ZAMS) masses: $M_\mathrm{ZAMS} = 13,
18, 21, 25, 35, 40$, and $45 M_\odot$. All of these models, at the onset of
core-collapse, feature steep density profiles, $\rho \propto r^{-\alpha}$ with
$\alpha\approx 2.5$, which would result in jets that are inconsistent with lGRB
observables. We follow the collapse of four out of our seven models until they
form BHs and the other three proto-neutron stars (PNSs). We find, across all
models, that the density profile outside of the newly-formed BH or PNS is
well-represented by a flatter power law with $\alpha \approx 1.35{-}1.55$. Such
flat density profiles are conducive to successful formation and breakout of
BH-powered jets and, in fact, required to reproduce observable properties of
lGRBs. Future models of lGRBs should be initialized with shallower
\textit{post-collapse} stellar profiles like those presented here instead of
the much steeper pre-collapse profiles that are typically used.
