  In this article we study correspondence between the microscopic spectrum and
macroscopic properties of a class of extremal and non-extremal black branes and
outline an origin of the interactions among various microstates of a given
black brane configuration from the perspective of an intrinsic Riemannian
geometry arising from the coarse graining entropy over a large number of
microstates. We have analyzed the state-space geometry in the case of various
extremal and non-extremal black branes arising from the string theories,
multi-centered black brane configurations, small black holes with fractional
branes, fuzzy rings in the set up of Mathur's fuzzballs and subensemble theory,
as well as that the black brane foams from the considerations of bubbling black
brane solutions in the M-theory. We have further shown that there exists a
clear mechanism on the black brane side that describes the notion of associated
interactions in the state-space or vice-versa. We thus find that in all such
cases there are no singularities in the state-space manifold of these black
brane configurations. This observation is in turn consistent with the existing
picture of corresponding microscopic CFT data.
