Extended uncertainty principle inspired black hole in a Gödel Universe
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916770414067712 |
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| author | Pantig, Reggie C. |
| author_facet | Pantig, Reggie C. |
| contents | 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 $ r_0 $. 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 $ r_0^2 / a^4 $. Series expansion in the limit $ a \to \infty $ 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 \sim 10^5 $, while solar system light-bending observations in the parametrized post-Newtonian (PPN) framework yield $ a / M_\odot \sim 5 \times 10^4 $. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended uncertainty principle inspired black hole in a Gödel Universe Pantig, Reggie C. General Relativity and Quantum Cosmology 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 $ r_0 $. 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 $ r_0^2 / a^4 $. Series expansion in the limit $ a \to \infty $ 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 \sim 10^5 $, while solar system light-bending observations in the parametrized post-Newtonian (PPN) framework yield $ a / M_\odot \sim 5 \times 10^4 $. 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. |
| title | Extended uncertainty principle inspired black hole in a Gödel Universe |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.00295 |