Using the strong field limit approach, the strong field gravitational lensing in a black hole with deficit solid angle (DSA) and surrounded by quintessence-like matter (QM) has been investigated. The results show that the DSA [Formula: see text], the energy density of QM [Formula: see text] and the equation of state (EOS) parameter [Formula: see text] have some distinct effects on the strong field gravitational lensing. As [Formula: see text] or [Formula: see text] increases, the deflection angle and the strong field limit coefficients all increase faster and faster. Moreover, the evolution of the main observables also has been studied, which shows that the curves at [Formula: see text] are more steepy than those of [Formula: see text]. Compared with the Schwarzschild black hole, the black hole surrounded by QM has smaller relative magnitudes, and at [Formula: see text] both the angular position and angular separation are slightly bigger than those of Schwarzschild black hole, but when [Formula: see text], the angular position and the relative magnitudes all diminish significantly. Therefore, by studying the strong gravitational lensing, we can distinguish the black hole with a DSA and surrounded by QM from the Schwarzschild black hole and the effects of the DSA and QM on the strong gravitational lensing by black holes can be known better.
Strong gravitational lensing for the photons coupled to Weyl tensor in a Schwarzschild black hole spacetime
