  There is probably not a black hole in the center of the sun. Despite this
detail, our goal in this work to convince the reader that this question is
interesting and that work studying stars with central black holes is well
motivated. If primordial black holes exist then they may exist in sufficiently
large numbers to explain the dark matter in the universe. While primordial
black holes may form at almost any mass, the asteroid-mass window between
$10^{-16} - 10^{-10} ~ \textrm{M}_\odot$ remains a viable dark matter candidate
and these black holes could be captured by stars upon formation. Such a star,
partially powered by accretion luminosity from a microscopic black hole in its
core, has been called a `Hawking star.' Stellar evolution of Hawking stars is
highly nontrivial and requires detailed stellar evolution models, which were
developed in our recent work. We present here full evolutionary models of solar
mass Hawking stars using two accretion schemes: one with a constant radiative
efficiency, and one that is new in this work that uses an adaptive radiative
efficiency to model the effects of photon trapping.
