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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18837765 |
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| _version_ | 1866902326158032896 |
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| author | Coates, David |
| author_facet | Coates, David |
| contents | <p>A Kerr (rotating) black hole possesses a Z2 reflection symmetry about its equatorial plane, dividing spacetime into two hemispheres of opposite gravitomagnetic polarity. We show that this bilateral structure is isomorphic to the eigenvalue decomposition of the Jacobsthal recurrence Tn+2 = Tn+1 + 2Tn, where the dominant root λ1 = 2 and subdominant root λ2 = −1 govern expansion and contraction modes separated by the stability boundary |Tr(M)| = 2. Two concrete numerical connections support this identification: (i) the innermost stable circular orbit (ISCO) of a Schwarzschild black hole sits at exactly 3rs, the Jacobsthal ratio J(3)/J(1) = 3, from the horizon; (ii) for Kerr spin parameter a∗ ≈ 0.7, the prograde ISCO descends to ≈ 5/3 Schwarzschild radii, matching the first non-trivial Jacobsthal convergent and the anomalous QPO ratio observed in GRS 1915+105. We propose that the Kerr spin parameter sweeps the ISCO through the Jacobsthal hierarchy, and that the bilateral north–south structure of the black hole maps onto the major/minor bilateral structure of the Universal Boundary framework. Falsification criteria and observational tests using gravitational-wave quasi-normal modes are specified.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18837765 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bilateral Structure of the Kerr Black Hole and Jacobsthal Stability Ratios Coates, David <p>A Kerr (rotating) black hole possesses a Z2 reflection symmetry about its equatorial plane, dividing spacetime into two hemispheres of opposite gravitomagnetic polarity. We show that this bilateral structure is isomorphic to the eigenvalue decomposition of the Jacobsthal recurrence Tn+2 = Tn+1 + 2Tn, where the dominant root λ1 = 2 and subdominant root λ2 = −1 govern expansion and contraction modes separated by the stability boundary |Tr(M)| = 2. Two concrete numerical connections support this identification: (i) the innermost stable circular orbit (ISCO) of a Schwarzschild black hole sits at exactly 3rs, the Jacobsthal ratio J(3)/J(1) = 3, from the horizon; (ii) for Kerr spin parameter a∗ ≈ 0.7, the prograde ISCO descends to ≈ 5/3 Schwarzschild radii, matching the first non-trivial Jacobsthal convergent and the anomalous QPO ratio observed in GRS 1915+105. We propose that the Kerr spin parameter sweeps the ISCO through the Jacobsthal hierarchy, and that the bilateral north–south structure of the black hole maps onto the major/minor bilateral structure of the Universal Boundary framework. Falsification criteria and observational tests using gravitational-wave quasi-normal modes are specified.</p> |
| title | Bilateral Structure of the Kerr Black Hole and Jacobsthal Stability Ratios |
| url | https://doi.org/10.5281/zenodo.18837765 |