  For a closed system to equilibrate from a given initial condition there must
exist an equilibrium state with the energy equal to the initial one.
Equilibrium states of a strongly coupled gauge theory with a gravitational
holographic dual are represented by black holes. We study the spectrum of black
holes in Pilch-Warner geometry. These black holes are holographically dual to
equilibrium states of strongly coupled $SU(N)$ ${\cal N}=2^*$ gauge theory
plasma on $S^3$ in the planar limit. We find that there is no energy gap in the
black hole spectrum. Thus, there is a priory no obstruction for equilibration
of arbitrary low-energy states in the theory via a small black hole
gravitational collapse. The latter is contrasted with phenomenological examples
of holography with dual four-dimensional CFTs having non-equal central charges
in the stress-energy tensor trace anomaly.
