Spacetime-curvature induced uncertainty principle: Linking the large-structure global effects to the local black hole physics

This paper links the advanced formulation of the Generalized Uncertainty Principle, termed the Asymptotic Generalized Extended Uncertainty Principle (AGEUP) to the corpuscular framework to derive the AGEUP-inspired black hole metric. The former incorporates spacetime curvature effects to explore black hole dynamics under quantum gravitational corrections, while the latter is a view that black holes are Bose–Einstein condensates of weakly interacting gravitons. AGEUP refines the traditional uncertainty relation by introducing curvature-based modifications that integrate the Ricci scalar and Cartan invariant, addressing the possible connection of the quantum uncertainties and gravitational influences in curved spacetimes. In particular, the phenomenological union between the AGEUP with cosmological constant Λ to the corpuscular framework enabled a black hole metric that has a scaled mass, which depends on Λ and the Planck length lPl. Interesting implications occur, such as the maximum limit for mass M where Λ ceases to influence the black hole. Another is the derived value of the modulation factor of the EUP term, α, if the large-scale fundamental length is defined solely as the cosmological horizon. We further analyze the black hole metric through the shadow and deflection angle phenomena, deriving constraints on the quantum gravity modulation parameter β that may be experimentally tested in future observations. Constraints from the Event Horizon Telescope (EHT) and Very Long Baseline Interferometry (VLBI) are discussed as avenues for verifying AGEUP-related deviations in black hole shadow radius and deflection angles, offering potential observational evidence of quantum gravitational effects at astrophysical scales. The findings suggest that AGEUP could be instrumental in providing hints on the quantum gravity nature of black holes, particularly in high-energy astrophysical contexts. By linking local black hole physics with large-scale curvature effects, AGEUP paves the way for further research at the intersection of quantum gravity and cosmology, with implications for observational astrophysics and the fundamental structure of spacetime.