Extended uncertainty principle inspired black hole in a G\"odel Universe

TL;DR

This paper develops a semiclassical black hole model in a G"odel universe using a curvature-modified extended uncertainty principle, revealing rotation-dependent effects on black hole features and constraining rotation parameters with astrophysical data.

Contribution

It introduces a novel curvature-modified EUP in a G"odel spacetime and derives analytical expressions for black hole properties, linking global rotation to observable signatures.

Findings

Rotation increases black hole observables compared to Schwarzschild.

Lower bounds on G"odel rotation parameter inferred from EHT data.

Rotation effects are observationally suppressed but theoretically significant.

Abstract

We explore analytically the implications of a curvature-modified extended uncertainty principle (EUP) derived in a rotating G\"odel spacetime and apply it to the construction of a semiclassical black hole model. Adapting techniques from corpuscular black hole frameworks, we reinterpret the G\"odel-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 G\"odel-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.