State-space correlations and stabilities

The state-space pair correlation functions and the notion of stability of extremal and nonextremal black holes in string theory and M theory are considered from the viewpoint of thermodynamic Ruppeiner geometry. We have explicitly analyzed the state-space configurations for (i) the two-and three-charge extremal black holes, (ii) the four-and six-charge nonextremal black branes, which both arise from the string theory solutions. An extension is considered for the D-6-D-4-D-2-D-0 multicentered black branes, fractional small black branes, and two-charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and the nature of stabilities have been investigated for three-charged bubbling black-brane foams, and thereby the M-theory solutions are brought into the present consideration. Novel aspects of the state-space interactions have been envisaged from the coarse graining counting entropy of underlying conformal field theory microstates.