On the Microscopic Perspective of Black Branes Thermodynamic Geometry

TL;DR

This paper explores the microscopic and macroscopic thermodynamic geometry of various black branes, revealing a consistent interaction structure and absence of singularities, aligning with microscopic CFT descriptions.

Contribution

It introduces an intrinsic Riemannian geometric framework to analyze interactions among microstates of diverse black brane configurations from string theory.

Findings

No singularities in the state-space manifold for studied black branes

Existence of a clear interaction mechanism in the state-space

Consistency with microscopic CFT data

Abstract

In this article we study correspondence between the microscopic spectrum and macroscopic properties of a class of extremal and non-extremal black branes and outline an origin of the interactions among various microstates of a given black brane configuration from the perspective of an intrinsic Riemannian geometry arising from the coarse graining entropy over a large number of microstates. We have analyzed the state-space geometry in the case of various extremal and non-extremal black branes arising from the string theories, multi-centered black brane configurations, small black holes with fractional branes, fuzzy rings in the set up of Mathur's fuzzballs and subensemble theory, as well as that the black brane foams from the considerations of bubbling black brane solutions in the M-theory. We have further shown that there exists a clear mechanism on the black brane side that describes the notion of associated interactions in the state-space or vice-versa. We thus find that in all such cases there are no singularities in the state-space manifold of these black brane configurations. This observation is in turn consistent with the existing picture of corresponding microscopic CFT data.