Shadow dependent phenomenology framework for rotating black hole metric
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| Format: | Preprint |
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2026
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| _version_ | 1866911621153030144 |
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| author | Lobos, Nikko John Leo S. Rodulfo, Emmanuel T. |
| author_facet | Lobos, Nikko John Leo S. Rodulfo, Emmanuel T. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22181 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shadow dependent phenomenology framework for rotating black hole metric Lobos, Nikko John Leo S. Rodulfo, Emmanuel T. General Relativity and Quantum Cosmology 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. |
| title | Shadow dependent phenomenology framework for rotating black hole metric |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.22181 |