Stars and black holes in varying speed of light theories

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.