We study the phase structure and equilibrium state space geometry of
R-charged black holes in D=5, 4 and 7 and the corresponding rotating D3,
M2 and M5 branes. For various charge configurations of the compact black
holes in the canonical ensemble we demonstrate new liquid-gas like phase
coexistence behaviour culminating in second order critical points. The critical
exponents turn out to be the same as that of four dimensional asymptotically
AdS black holes in Einstein Maxwell theory. We further establish that the
regions of stability for R-charged black holes are, in some cases, more
constrained than is currently believed, due to properties of some of the
response coefficients. The equilibrium state space scalar curvature is
calculated for various charge configurations, both for the case of compact as
well as flat horizons and its asymptotic behaviour with temperature is
established.Comment: 1 + 33 pages, LaTeX, 25 figures. References adde