Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma

In this study,the gravitational deflection angle of photons in the weak field limit（or the weak deflection angle） and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole（BH） in the string cloud background are investigated.The influences of the BH charge Q,quintessence parameter γ,and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem.in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the chargedKiselev BH in string clouds.Moreover,we study the effects of plasma（uniform and non-uniform） on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings.In the presence of a uniform/nonuniform plasma medium,an increase in the string cloud parameter a increases the deflection angle α.In contrast,a decrease in the BH charge Q decreases the deflection angle.Further,we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH.We notice that,with an increase in the values of the parameters γ and a,the size of the BH shadow increases,and therefore,the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases.Thus,the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH.Moreover,we use the data released by the Event Horizon Telescope（EHT） collaboration,for the supermassive BHs M87* and Sgr A*,to obtain constraints on the values of the parameters γ and a.