  Low-metallicity (Z <~ 0.05 Zsun) massive (>~40 Msun) stars might end their
life by directly collapsing into massive black holes (BHs, 30 <~ m_BH/Msun <~
80). More than ~10^5 massive BHs might have been generated via this mechanism
in the metal-poor ring galaxy Cartwheel, during the last ~10^7 yr. We show that
such BHs might power most of the ultra-luminous X-ray sources (ULXs) observed
in the Cartwheel. We also consider a sample of ULX-rich galaxies and we find a
possible anti-correlation between the number of ULXs per galaxy and the
metallicity in these galaxies. However, the data are not sufficient to draw any
robust conclusions about this anti-correlation, and further studies are
required.
