Constraining the generalized uncertainty principle through black hole shadow, S2 star orbit, and quasiperiodic oscillations

In this paper, we study the effect of the Generalized Uncertainty Principle (GUP) on the shadow of GUP-modified Kerr black hole and the correspondence between the shadow radius and the real part of the quasinormal modes (QNMs). We find that the shadow curvature radius of the GUP-modified Kerr black hole is bigger compared to the Kerr vacuum solution and increases linearly monotonically with the increase of the GUP parameter. We then investigate the characteristic points of intrinsic curvature of the shadow from a topological point of view to calculate the angular size for these curvature radii of the shadow. To this end, we have used the EHT data for the M87* black hole to constrain the upper limits of the GUP parameter and our result is beta < 10(95). Finally, we have explored the connection between the shadow radius and the scalar/electromagnetic/gravitational QNMs. Using the orbit of S2 star we have obtained a bound for the GUP parameter beta < 10(87). The GUP-modified Kerr black hole is also used to provide perfect curve fitting of the particle oscillation upper and lower frequencies to the observed frequencies for three microquasars and to restrict the values of the correction parameter in the metric of the modified black hole to very reasonable bound beta < 10(77).

Automated summary

This paper investigates the effects of the Generalized Uncertainty Principle (GUP) on the shadow and quasinormal modes (QNMs) of GUP-modified Kerr black holes. The study reveals that the GUP modification increases the curvature radius of the shadow and that it increases linearly with the GUP parameter. By using observational data and fitting techniques, the upper limits of the GUP parameter and the correction parameter in the modified black hole metric are determined.