Geodesics around oscillatons made of exponential scalar field potential

Abstract

Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around an oscillaton related to a time dependent scalar field. Bound orbital is found for these particles under the condition of particular values of angular momentum L and initial radial position. We discuss this topic for an exponential scalar field potential which could be of the exponential form with a scalar field and investigate whether the radial coordinates of such particles oscillate in time or not and thereby we could predict the corresponding oscillating period as well as amplitude. It is necessary to recall, in general relativity, a geodesic generalizes the notion of a straight line to curved space time. Importantly, the world line of a particle free from all external, non gravitational forces, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved space time geometry where the source of curvature is the stress energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4D space time geometry around the star onto 3D space.