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This research aims to explore how geometric properties around black holes reveal information about their gravitational acceleration and Hawking radiation.

June 8, 2026Open Access

Paper LXXIX: Spacetime Monodromy Around a Black Hole as a Focal Zone: Gravitational Acceler- ation, Hawking Radiation, the Z3 Colour Origin of ln 3 in the Highly-Damped QNM Spectrum, and the e7 Horizon Monodromy of the Fano Brane Current

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This research aims to explore how geometric properties around black holes reveal information about their gravitational acceleration and Hawking radiation.
Utilized a theoretical framework based on octonionic geometry to analyze black holes, focusing on monodromy effects.
Derived gravitational acceleration and Hawking temperature expressions from the geometric properties around black holes.
Investigated the relationship between QNM spectrum factors and the colour symmetry in the context of black hole physics.
Hawking temperature was derived from e7 monodromy yielding TH = ℏκ/2πkB.
Gravitational acceleration formulations were established, showing g = GM/r² in Newtonian and g = √GMa₀/r in MOND regimes.
Identified ln 3's origin in the QNM spectrum linked to the Fano colour symmetry structure.

Abstract

The monodromy of a geometric object under parallel transport around a closed loop encircling a singularity encodes deep information about the black hole: both its gravitational acceleration eld (imaginary part of the null geodesic holonomy) and its Hawking radiation temperature (monodromy phase of the Bogoliubov transformation). In the brane-bulk octonionic framework, a black hole is a maximal focal zone with the e7 Fano node serving as the algebraic separator between the H+ matter sector and the H−bulk beyond the horizon. We derive three results. (1) Hawking temperature from e7 monodromy. The e7 crossing generates a Z2 monodromy Me7 = −1. One complete loop through the e7 node accumulates phase 2πω/κ, giving TH = ℏκ/2πkB. (2) Gravitational acceleration from null geodesic holonomy. The imaginary part of H kr dr around the focal zone gives g = GM/r2 in the Newtonian regime and g = √GMa0/r in the MOND regime (Paper LVII). (3) The factor ln 3 in the highly- damped QNM spectrum has a Fano colour-sector origin. Motl and Neitzke? ,? showed that highly-damped Schwarzschild QNMs satisfy 8πMω = ± ln 3 −iπ (2n + 1). The factor ln 3 arises from the monodromy of the wave equation around r = 0, which gives (1 + 2 cos πs) = 3 for s = 0, 2. In the Fano framework, this factor 3 is the order of the Z3 colour symmetry group acting on the nodes e4, e5, e6 ⊂H−: the monodromy around the central singularity encodes the algebraic structure of the colour sector. The imaginary spacing π (2n + 1) contains the Z2 monodromy phase π of the e7 crossing, giving the half-integer oset characteristic of a one-sided topological barrier (Paper LXXX, Prediction 181). The KSS viscosity bound η/s = ℏ/4πkB derivable from the hydrodynamic QNM of the AdS black brane (Berti, Cardoso, Starinets? ) is the holographic dual of the brane fabric viscosity minimum at the Weissenberg crossover Wi = 1 (Paper LI). Four new predictions follow (Predictions 176179). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.

Paper LXXIX: Spacetime Monodromy Around a Black Hole as a Focal Zone: Gravitational Acceler- ation, Hawking Radiation, the Z3 Colour Origin of ln 3 in the Highly-Damped QNM Spectrum, and the e7 Horizon Monodromy of the Fano Brane Current

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