On the Microscopic Perspective of Black Branes Thermodynamic Geometry

We study thermodynamic state-space geometry of the black holes in string theory and M -theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and subensemble theory. We extend our analysis for the black brane foams and bubbling black brane solutions in M -theory. We discuss the nature of state-space correlations of various black brane configurations, and show that the notion of state-space manifolds describes the associated coarse-grained interactions of the corresponding microscopic CFT data.