BLACK STRINGS, BLACK RINGS AND STATE-SPACE MANIFOLD

State-space geometry is considered, for diverse three and four parameter nonspherical horizon rotating black brane configurations, in string theory and M-theory. We have explicitly examined the case of unit Kaluza-Klein momentum D1D5P black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, viz. the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a nondegenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating D1D5 black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued M-5-dipole charged rotating circular strings and Maldacena-Strominger-Witten black rings exhibit nondegenerate, positively curved, comprehensively regular state-space configurations. Furthermore, the state-space geometry of single bubbled rings admits a well-defined, positive definite, everywhere regular and curved intrinsic Riemannian manifold; except for the two finite values of conserved electric charge. We also discuss the implication and potential significance of this work for the physics of black holes in string theory.