  We search for stable bound states of non-extremal rotating three-charge black
holes in five dimensions (Cvetic-Youm black holes) and supertubes. We do this
by studying the potential of supertube probes in the non-extremal black hole
background and find that generically the marginally bound state of the
supersymmetric limit becomes metastable and disappears with non-extremality
(higher temperature). However near extremality there is a range of parameters
allowing for stable bound states, which have lower energy than the
supertube-black hole merger. Angular momentum is crucial for this effect. We
use this setup in the D1-D5 decoupling limit to map a thermodynamic instability
of the CFT (a new phase which is entropically dominant over the black hole
phase) to a tunneling instability of the black hole towards the supertube-black
hole bound state. This generalizes the results of ArXiv:1108.0411 [hep-th],
which mapped an entropy enigma in the bulk to the dual CFT in a supersymmetric
setup.
