  We present fully general-relativistic numerical evolutions of
self-gravitating tori around spinning black holes with dimensionless spin $a/M
= 0.7$ parallel or anti-parallel to the disk angular momentum. The initial
disks are unstable to the hydrodynamic Papaloizou-Pringle Instability which
causes them to grow persistent orbiting matter clumps. The effect of black hole
spin on the growth and saturation of the instability is assessed. We find that
the instability behaves similarly to prior simulations with non-spinning black
holes, with a shift in frequency due to spin-induced changes in disk orbital
period. Copious gravitational waves are generated by these systems, and we
analyze their detectability by current and future gravitational wave
observatories for large range of masses. We find that systems of $10 M_\odot$ -
relevant for black hole-neutron star mergers - are detectable by Cosmic
Explorer out to $\sim300$ Mpc, while DECIGO (LISA) will be able to detect
systems of $1000 M_\odot$ ($10^5M_\odot$) - relevant for disks forming in
collapsing supermassive stars - out to cosmological redshift of $z\sim5$
($z\sim 1$). Computing the accretion rate of these systems we find that these
systems may also be promising sources of coincident electromagnetic signals.
