Null geodesics and shadow of 4D Einstein–Gauss–Bonnet black holes surrounded by quintessence

Abstract

We study the properties of the null geodesics of four-dimensional Einstein–Gauss–Bonnet (4D EGB) black holes surrounded by quintessence matter, recently derived by Shah et al. [Phys. Lett. B 818 (2021) 136383]. Due to the quintessence correction, we discuss the radial and nonradial geodesics. For the case of nonradial geodesics we obtain the effective potential, photon sphere and impact parameter associated to the null geodesics in detail. We analyze the different possible orbits of massless particles (i.e. photons) such as unstable circular orbits and unbounded orbits and investigate the role of the Gauss–Bonnet coupling [Formula: see text] and the quintessence parameter q on the null geodesic trajectories. Moreover, we study the effects of the model parameters on the shadow cast by such black holes. The results are compared to that of Schwarzschild black hole with and without quintessence matter and 4D EGB black holes without quintessence. As a physical application of null geodesics, the deflection angle is calculated and the effect of the quintessence matter on it is investigated.