Extended uncertainty principle inspired black hole in a Gödel Universe

2025/05/30 by Reggie C. Pantig, Pantig, Reggie C.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2506.00295

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore analytically the implications of a curvature-modified extended uncertainty principle (EUP) derived in a rotating Gödel spacetime and apply it to the construction of a semiclassical black hole model. Adapting techniques from corpuscular black hole frameworks, we reinterpret the Gödel-type uncertainty relation as an effective energy bound, leading to a modified lapse function with explicit dependence on the global rotation parameter a and the radial coordinate r₀ . Analytic expressions are derived for key gravitational features, including the event horizon, photon spherehere, shadow radius, and deflection angle, with curvature corrections scaling as a^-2 and r₀² / a⁴ . Series expansion in the limit a → ∞ shows that global rotation consistently increases all observables relative to the Schwarzschild case. Applying these results to astrophysical data, we use Event Horizon Telescope (EHT) measurements of Sgr A* and M87* to infer lower bounds of a/M ∼ 10⁵ , while solar system light-bending observations in the parametrized post-Newtonian (PPN) framework yield a / M_\odot ∼ 5 × 10⁴ . These large but finite values validate the asymptotic expansion and confirm that Gödel-type rotation remains observationally suppressed, yet theoretically coherent. Our results demonstrate that global rotation, when treated semiclassically via curvature-modified uncertainty, introduces detectable signatures in principle, though well below current observational sensitivity. The framework offers a consistent path toward exploring the quantum-gravitational interplay between global geometry and local black hole structure.

Citations

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• Uncertainty Principles and Non-local Black Holes

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