Generalized Extended Uncertainty Principle Black Holes: Shadow and lensing in the macro- and microscopic realms

TL;DR

This paper explores the effects of the Generalized Extended Uncertainty Principle (GEUP) on black hole shadows and gravitational lensing, providing constraints on fundamental length scales and analyzing differences between astrophysical and micro-black holes.

Contribution

It extends the study of EUP black holes to GEUP, deriving shadow radii, constraining length scales with observational data, and analyzing lensing effects in macro and micro realms.

Findings

GEUP increases shadow radius for astrophysical black holes

Constraints on fundamental length scale L* from EHT data

Weak lensing is more sensitive in micro-black hole regime

Abstract

Motivated by the recent work about the Extended Uncertainty Principle (EUP) black holes \cite{Mureika:2018gxl}, we present in this study its extension called the Generalized Extended Uncertainty Principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and micro-black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale $L*$ up to $2\sigma$ level were also found using the EHT data: for Sgr. A*, $L* = 5.716\text{x}10^{10}$ m, while for M87*, $L* = 3.264\text{x}10^{13}$ m. Under the GEUP effect, the value of the shadow radius behaves the same way as the Schwarzschild case due to a static observer, and the effect only emerges if the mass of the black hole $M$ is around the order of magnitude of $L_*$ (or $l_\text{Pl}$). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for micro-black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of $L_*$ and $M$ are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world.