Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.