The analytical discussion on strong gravitaional lensing for a gravitational source with a $f(R)$ global monopole

TL;DR

This paper analyzes strong gravitational lensing caused by a Schwarzschild black hole with a global monopole in $f(R)$ gravity, deriving explicit formulas for deflection angles and time delays, and exploring observable deviations from standard general relativity.

Contribution

It provides explicit expressions for lensing observables in $f(R)$ gravity with a global monopole, highlighting how small modifications can produce measurable effects.

Findings

Deflection angle and time delay depend on monopole and $f(R)$ correction $ extpsi_0$

Explicit formulas for strong field lensing observables are derived

Tiny deviations from GR can lead to significant observational signatures

Abstract

Here the gravitational lensing in strong field limit of a Schwarzschild black hole with a solid deficit angle owing to global monopole within the context of the $f(R)$ gravity theory is investigated. We obtain the expressions of deflection angle and time delay in the forms of elliptic integrals and discuss the asymptotic behaviour of the elliptic integrals to find the explicit formulae of angle and time difference in the strong field limit. We show that the deflection angle and the time delay between multiple images are related not only to the monopole but also to the $f(R)$ correction $\psi_{0}$ by taking the cosmological boundary into account. Some observables such as the minimum impact parameter, the angular separation, the relative magnification and the compacted angular position have been estimated as well. It is intriguing that the tiny modification on the standard general relativity will make the remarkable deviation on the angle and the time lag, offering a significant way to explore some possible distinct signatures of the topological soliton and the correction of the Einstein general relativity.