BLACK STRINGS, BLACK RINGS AND STATE-SPACE MANIFOLD

STEFANO BELLUCCI, BHUPENDRA NATH TIWARI
2011 International Journal of Modern Physics A  
State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and M-theory. We have explicitly examined the case of unit Kaluza-Klein momentum D_1D_5P 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
more » ... ic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating D_1D_5 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 non-degenerate, 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.
doi:10.1142/s0217751x11054978 fatcat:h7m6henzevcqnfllqmvmi2hhre