E. L. B. Junior, F. S. N. Lobo, M. E. Rodrigues, H. A. Vieira
Abstract
In this paper we study the gravitational lensing effect for the Schwarzschild solution with holonomy corrections. We use two types of approximation methods to calculate the deflection angle, namely the weak and strong field limits. For the first method, we calculate the deflection angle up to the fifth order of approximation and show the influence of the parameter λ (in terms of loop quantum gravity) on it. In addition, we construct expressions for the magnification, the position of the lensed images and the time delay as functions of the coefficients from the deflection angle expansion. We find that λ increases the deflection angle. In the strong field limit, we use a logarithmic approximation to compute the deflection angle. We then write four observables, in terms of the coefficients b1, b2, and um, namely: the asymptotic position approached by a set of images θ∞, the distance between the first image and the others s , the ratio between the flux of the first image and the flux of all other images rm, and the time delay between two photons ΔT2,1. We then use the experimental data of the black hole Sagittarius A⋆ and calculate the observables and the coefficients of the logarithmic expansion. We find that the parameter λ increases the deflection angle, the separation between the lensed images and the delay time between them. In contrast, it decreases the brightness of the first image compared to the others.
Keywords
General relativity; Particles & Fields
Physical Review D
Volume 109, Issue 2, Page 26
2024 January
