For nearly a century Black holes have been a hot topic, a physical singularity or simply a flawed, all be it brilliant, mathematical concept? Fundamental proof of the existence of black holes lies in the proof of the existence of their event horizons. One such proof lies in the comparison of the X-ray luminosities of black hole and neutron star X-ray transients however this proof assumes that both NS and BH transients continue to accrete at low Mdot during quiescence. Cen X-4 is the prototype NS X-ray transient, and this work is compared to A06020-00, the prototype BH X-ray Transient. As part of this comparison we obtained the first short-wavelength UV spectrum of Cen X-4 in 2004 with HST STIS and obtained simultaneous X-ray data with Chandra. Interestingly, the X-ray flux was found to decrease by a factor of three, while the UV was down by a factor of two. We report on our search for evidence for a disk in the UV and optical spectra, even at these very low Mdot levels. We have extracted the highest quality spectrum from the HST STIS and Chandra data, and compared Cen X -4 to A0620, searching for hints as to the accretion, emission mechanisms and ultimately the existence of their event horizons. This research as been jointly funded by the University of Southampton and the Harvard-Smithsonian center for astrophysics.