Algebraic Structures in Black Hole Spectral Theory: Connections Between the Isomonodromic Method and the Category of Informational Structures

This work proposes a theoretical framework connecting algebraic and categorical structures with the spectral theory of black hole quasinormal modes. Using C*-algebras and higher category theory, the article identifies structural correspondences between the isomonodromic method and a category of informational structures (InfoStr), in which physical theories are represented as pairs consisting of observable algebras and state spaces. Within this framework, the Riemann–Hilbert correspondence is interpreted as a functor between informational categories, isomonodromic deformations appear as natural transformations, and the Jimbo–Miwa–Ueno τ-function acquires the role of a categorical invariant. The work further proposes a categorical interpretation of exceptional points in Kerr black hole spectra as singularities of a 2-groupoid structure, relating the observed Z₂ Berry phase to a Postnikov-type holonomy. Additional connections are explored between trace functor formalism and greybody factors, as well as between modular flow, black hole entropy, and quasinormal mode spectra. The results are presented as a combination of reformulations of known structures and proposals for further investigation, intended to stimulate collaboration at the interface between operator algebras, integrable systems, and gravitational physics.