Shadow dependent phenomenology framework for rotating black hole metric

TL;DR

This paper introduces a duality linking black hole quantum evaporation with classical geometry, enabling observable-based parameterization and revealing model-specific phenomenological signatures in rotating black holes.

Contribution

It develops a novel framework connecting black hole thermodynamics and optics, allowing direct inference of classical and semiclassical properties from shadow observations, and distinguishes effects of modified gravity.

Findings

Standard Kerr luminosity scales as R_sh^{-2} under EHT constraints.

Modified gravity alters deflection and Hawking radiation signatures.

Horndeski scalar hair causes up to 52% deviation in Hawking emission.

Abstract

We establish a thermodynamic-optical duality that directly bridges the semiclassical quantum evaporation of black holes with their classical macroscopic geometry. By employing a diffeomorphic inversion, we re-parameterize the intrinsic black hole mass entirely in terms of the observable shadow radius $R_{sh}$. This mapping allows the formulation of the classical weak deflection angle, Hawking temperature, and integrated semiclassical luminosity, bypassing the unobservable bare mass. Applying this methodology to the standard Kerr, Kerr-MOG, and rotating Horndeski spacetimes, we reveal distinct, model-specific phenomenological signatures. For a statistically fixed shadow radius constrained by Event Horizon Telescope (EHT) observations of M87*, the standard Kerr geometry yields a baseline luminosity scaling of $L \propto R_{sh}^{-2}$. In modified gravity regimes, the duality breaks the degeneracy between bare mass and modified field strengths: the MOG repulsive vector field enhances classical deflection while strictly suppressing quantum luminosity, whereas Horndeski scalar hair introduces a unique logarithmic augmentation to astrometric lensing and drives up to a $\sim 52\%$ deviation in Hawking emission under current EHT limits. By strictly anchoring theoretical observables to empirical interferometric boundaries, this framework provides a computationally efficient avenue for testing the Kerr hypothesis and probing fundamental fields in strong-field gravity.