A Primer of State-space Geometry

In this Primer, we offer black hole thermodynamics and physics of extremal and non-extremal black holes in from the perspective of the statistical correlations and brane-antibrane configurations. Given a string theory black hole configuration, the framework of the intrinsic state-space geometry shows that the stability of charged anticharged black brane solutions are encoded in the positivity of principle minors of the space-state metric tensor. We provide the local and global stability structures of rotating black holes, black strings, black rings, multi-centered black branes, 1/2-BPS configurations, brane fractionation, Mathur's Fuzzball solutions, subensemble theory in string theory and bubbling black brane foams in M-theory. We discuss perspective implications towards the intrinsic geometric understanding of the vacuum fluctuations and physics of brane-antibrane bound states in string theory.