Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*

Abstract

We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is taken into account, leading to a more general formulation also known as the Generalized Uncertainty Principle. Using as probe electromagnetic waves acquiring orbital angular momentum when lensed by a rotating black hole, we find from numerical simulations a relationship between the spectrum of the orbital angular momentum of light and the corrections needed to formulate the Generalized Uncertainty Principle, here characterized by the rescaled parameter ${\beta }_0$, a function of the Planck's mass and the bare mass of the black hole. Then, from the analysis of the observed twisted light due to the gravitational field of the compact object observed in M87*, we find new limits for the parameter ${\beta }_0$. With this method, complementary to black hole shadow circularity analyses, we obtain more precise limits from the experimental data of M87*, confirming the validity of scenarios compatible with General Relativity, within the uncertainties due to the experimental errors present in EHT data and those due to the numerical simulations and analysis.

5 pages, 2 figures. v2: typos corrected

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