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Motivated by black hole solutions with matter fields outside their horizon,we study the effect of these matter fields in the motion of massless andmassive particles. We consider as background a four-dimensional asymptoticallyAdS black hole with scalar hair. The geodesics are studied numerically and wediscuss about the differences in the motion of particles between thefour-dimensional asymptotically AdS black holes with scalar hair and theirno-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found thatthere are bounded orbits like planetary orbits in this background. However, theperiods associated to circular orbits are modified by the presence of thescalar hair. Besides, we found that some classical tests such as perihelionprecession, deflection of light and gravitational time delay have the standardvalue of general relativity plus a correction term coming from the cosmologicalconstant and the scalar hair. Finally, we found a specific value of theparameter associated to the scalar hair, in order to explain the discrepancybetween the theory and the observations, for the perihelion precession ofMercury and light deflection.

Motion of particles on a Four-Dimensional Asymptotically AdS Black Hole with Scalar Hair