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

Abstract: We study the properties of the null geodesics of four-dimensional Einstein-Gauss-Bonnet black holes surrounded by quintessence matter. Due to the quintessence correction, we discuss the radial and non-radial geodesics. For the case of non-radial geodesics we obtain the effective potential, the photon sphere and the impact parameter associated to the null geodesics in details. 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 $\alpha$ and the quintessence parameter $q$ on the null geodesic trajectories. Moreover, we also study the effects of the model parameters on the shadow cast by theses black holes. The results are compared with the Schwarzschild black hole with and without quintessence matter and four-dimensional Einstein-Gauss-Bonnet black holes without quintessence. As a physical application of the null geodesics, the deflection angle is calculated and the effect of the quintessence matter on it is investigated.