  We investigate spherically symmetric solutions to a recently proposed
covariant and locally Lorentz-invariant varying speed of light theory. We find
the metrics and variations in $c$ associated with the counterpart of black
holes, the outside of a star, and stellar collapse. The remarkable novelty is
that $c$ goes to zero or infinity (depending on parameter signs) at the
horizon. We show how this implies that, with appropriate parameters, observers
are prevented from entering the horizon. Concomitantly stellar collapse must
end in a ``Schwarzchild radius'' remnant. We then find formulae for
gravitational light deflection, gravitational redshift, radar echo delay, and
the precession of the perihelion of Mercury, highlighting how these may differ
distinctly from their Einstein counterparts but still evade experimental
constraints. The main tell-tale signature of this theory is the prediction of
the observation of a different value for the fine structure constant, $\alpha$,
in spectral lines formed in the surface of stars. We close by mentioning a
variety of new classical and quantum effects near stars, such as aging
gradients and particle production.
