  The hoop conjecture, introduced by Thorne almost five decades ago, asserts
that black holes are characterized by the mass-to-circumference relation $4\pi
{\cal M}/{\cal C}\geq1$, whereas horizonless compact objects are characterized
by the opposite inequality $4\pi {\cal M}/{\cal C}<1$ (here ${\cal C}$ is the
circumference of the smallest ring that can engulf the self-gravitating compact
object in all azimuthal directions). It has recently been proved that a
necessary condition for the validity of this conjecture in horizonless
spacetimes of spatially regular charged compact objects is that the mass ${\cal
M}$ be interpreted as the mass contained within the engulfing sphere (and not
as the asymptotically measured total ADM mass). In the present paper we raise
the following physically intriguing question: Is it possible to formulate a
unified version of the hoop conjecture which is valid for both black holes and
horizonless compact objects? In order to address this important question, we
analyze the behavior of the mass-to-circumference ratio of Kerr-Newman black
holes. We explicitly prove that if the mass ${\cal M}$ in the hoop relation is
interpreted as the quasilocal Einstein-Landau-Lifshitz-Papapetrou and Weinberg
mass contained within the black-hole horizon, then these charged and spinning
black holes are characterized by the sub-critical mass-to-circumference ratio
$4\pi {\cal M}/{\cal C}<1$. Our results provide evidence for the non-existence
of a unified version of the hoop conjecture which is valid for both black-hole
spacetimes and spatially regular horizonless compact objects.
