Probing Effective Loop Quantum Gravity on Weak Gravitational Lensing, Hawking Radiation and Bounding Greybody Factor by Black Holes

TL;DR

This paper explores the effects of loop quantum gravity on black hole phenomena, including gravitational lensing, Hawking radiation, and greybody factors, revealing how quantum corrections influence these observable properties.

Contribution

It introduces a novel analysis of black hole properties within effective loop quantum gravity, incorporating plasma and dark matter effects, and provides graphical insights into these quantum gravitational effects.

Findings

Deflection angle increases with plasma and dark matter mediums.

Hawking temperature and greybody bounds are computed using Gauss-Bonnet theorem.

Quantum corrections reduce to Schwarzschild solutions when the parameter is zero.

Abstract

In this paper, we study the weak deflection angle of black hole in effective loop quantum gravity using the geometrical technique used by Gibbons and Werner. We first derive the optical metric, calculate the Gaussian optical curvature, and then apply the Gauss-Bonnet theorem. We then also investigate the effect of plasma and dark matter mediums on the weak deflection angle. We show that increasing the impact of these two mediums grows the deflection angle. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the deflection angle and bounds on the greybody factor. Graphically, we observe that taking $0 < A_{\lambda} < 1$ angle ranges from negative values to maximum values and also attain maximum value for these values of $ A_{\lambda}$ and for $A_{\lambda} \geq 1$ exponentially approaches to zero. Later, we graphically investigate that the greybody factor bound exhibits the convergent behaviour by converging to $1$. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduced to the Schwarzschild black hole solutions when the dimensionless non-negative parameter is equal to zero $A_{\lambda}=0$.