Study of null geodesics and their stability in Horndeski black holes

Abstract We study the motion of particles in the background of a scalar–tensor theory of gravity in which the scalar field is kinetically coupled to the Einstein tensor, and we present the null geodesic structure for asymptotically flat, AdS, and dS Horndeski black holes, studying the effect of the cosmological constant on the orbits. Also, we consider three classical tests of gravity in the solar system, namely the bending of the light, the gravitational redshift, and the Shapiro time delay, in order to constraint the coupling parameters of the scalar field to gravity. Calculating the Lyapunov exponent, we explore the stability of these geodesics for various values of the cosmological constant.