  We study some general properties of two black hole solutions in Einstein's
conformal gravity. Both solutions can be obtained from the Kerr metric with a
suitable conformal rescaling, which leads, respectively, to a regular and a
singular spacetime. In addition to the mass $M$ and the spin angular momentum
$J$ of the black hole, these solutions are characterized by a new parameter,
$L$, which may be expected to be of the order of the black hole mass. We study
the geodesic motion and we calculate the radiative efficiency of a putative
accretion disk around these black holes, which allows us to get an estimate of
an upper bound on the value of $L$. Lastly, we explore the possibility of
"destroying" the event horizon of these black holes. Within our approach, we
are not able to destroy the event horizon of the regular black hole solution,
while we can in the case of the singular one.
