Black Strings, Black Rings and State-space Manifold

TL;DR

This paper explores the state-space geometry of various non-spherical horizon black brane configurations in string and M-theory, revealing different geometric properties and correlations that could impact black hole physics.

Contribution

It provides a detailed analysis of the intrinsic Riemannian geometry of diverse black brane solutions, identifying conditions for degenerate and non-degenerate state-space manifolds.

Findings

Degenerate state-space for certain black strings and rings.

Non-degenerate, positively curved state-space for others.

Regular, well-defined geometry for single bubbled rings except at specific charges.

Abstract

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, {\it viz.}, the first category divulges a degenerate intrinsic 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.