Analytical discussion on strong gravitational lensing for a massive source with a f(R) global monopole

Here we investigate the gravitational lensing in the strong field limit of a Schwarzschild black hole with a solid deficit angle owing to a global monopole within the context of the f(R) gravity theory. We obtain the expressions of the deflection angle and time delay in the forms of elliptic integrals and discuss the asymptotic behavior of the elliptic integrals to find the explicit formulas of the 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 are estimated as well. It is intriguing that a tiny modification on standard general relativity will make a 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 Einstein's general relativity.