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

In this paper we investigate the influence of the dark energy on thetime-like geodesic motion of a particle in Schwarzschild spacetime byanalysing the behaviour of the effective potential which appears inan equation of motion. For the non-radial time-like geodesics, wefind a bound orbit when the particle energy is in an appropriaterange, and also find another possible orbit, which is that theparticle drops straightly into the singularity of a black hole orescapes to infinity. For the radial time-like geodesics, we find anunstable circular orbit when the particle energy is the criticalvalue, in which case it is possible for the particle to escape toinfinity.