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

F Tamburini,F Feleppa,B Thidé

doi:10.1016/j.physletb.2022.136894

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 probes 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 β0, 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 β0. 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.

Highlights

Most of the knowledge we have about our Universe is obtained by extracting the information encoded in the spectrum of electromagnetic (EM) waves emitted by celestial bodies and, more recently, from neutrinos and gravitational waves in the framework of multi-messenger astronomy [1,2,3], including new phenomena observed at extremely high energies and in strong gravitational fields, where the classical formulation of the Heisenberg uncertainty principle (HUP) can loose its validity
Merical simulations that the Generalized Uncertainty Principle (GUP) parameter is restricted in the interval 0 < β0 ≤ 0.01064. This shows that the use of the additional information encoded in the phase of orbital angular momentum (OAM) beams allows us to extract more information from the experimental data, obtaining a better upper limit to the value of the GUP parameter β0, smaller than two up to three orders of magnitude than the one previously estimated with rotating black hole (BH)
In this letter we have determined a new upper limit on the GUP parameter β0 = β/2M 2 thanks to the OAM analysis of the twisted light from the compact object observed in M87* [59, 67] by the Event Horizon Telescope collaboration [61,62,63,64,65,66]

Summary

INTRODUCTION

Most of the knowledge we have about our Universe is obtained by extracting the information encoded in the spectrum of electromagnetic (EM) waves emitted by celestial bodies and, more recently, from neutrinos and gravitational waves in the framework of multi-messenger astronomy [1,2,3], including new phenomena observed at extremely high energies and in strong gravitational fields, where the classical formulation of the Heisenberg uncertainty principle (HUP) can loose its validity. To determine the effects of the GUP-corrected gravitational field, we fixed the size of the accretion disk’s (AD) to rdisk = 10, given in units of BH masses of an ideal Kerr BH, and the rotation parameter a = 0.85 with inclination i = 17◦ It is immediately evident, as seen in the upper panels of Fig. 1, that the result of the gravitational lensing due to a rotating compact object in the presence of gravitational GUP corrections appears different from that of a Kerr BH described by the standard equations of GR. The more the GUP parameter β0 increases, the more the corresponding (a, q) curve is confined to lower regions of the plot, towards values of the parameter q This effect clearly indicates that the rotation of the compact object is less effective in the transfer of OAM to the lensed light because of the GUP corrections. To determine the limits to β0 we take as reference the 95% confidence zone defined by the analysis of M87* OAM data, and we find from the nu-

Comparison with EHT data analysis

CONCLUSION