  Five dimensional Einstein gravity vacuum solutions in general fall into two
classes of black rings with horizon topology S^2 \times S^1, and black holes
with horizon topology S^3. These solutions are specified by their mass and two
spins. There are "overlapping" regions of this parameter space where one has
extremal rings and holes of the same spins. We show that for such regions the
hole has generically a larger entropy than the ring, and likewise, the central
charge of the proposed chiral 2d CFT dual to the hole is larger than that of
the ring. For special places of this overlapping region where one of the spins
tends to zero, the entropies of the extremal ring and hole also tend to zero
and essentially become equal. In this case we are dealing with Extremal
Vanishing Horizon (EVH) black holes or rings. The near horizon geometry of the
near-EVH hole and rings both contain locally AdS_3 throats, providing a basis
for the EVH/CFT proposal, a 2d CFT description of the low energy excitations of
EVH hole or ring. We argue how the near-EVH hole and near-EVH ring can be
distinguished from this dual 2d CFT viewpoint: The hole is a thermal state with
zero temperature in the left sector and finite temperature in the right, while
the ring is a generic state in the ground state (of the CFT on the plane) in
the left sector and a thermal state in the right. The latter is part of the
Hilbert space of the 2d CFT obtained in the Discrete Light Cone Quantization
(DLCQ).
