Abstract
Some of the spherically symmetric solutions to the Einstein–Klein–Gordon (EKG) equations can describe the astronomical soliton objects made of a real time-dependent scalar fields. The solutions are known as oscillatons which are non-singular satisfying the flatness conditions asymptotically with periodic (separated) time-dependency. In this paper, we investigate the geodesic motion around an oscillaton. The Spherically Symmetric Geometry allows the bound orbits in the plan \(\theta=\frac{\pi}{2}\) under a given initial conditions. The potential for the scalar field \(\varPhi=\varPhi(r,t)\), is an exponential function of the form \(V(\varPhi)=V_{0}\exp(\lambda\sqrt{k_{0}}\varPhi)\).
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Notes
In the Einstein equations, \(k_{0}=8\pi G=\frac{8\pi}{m_{Pl}^{2}}\), where the gravitational constant, \(G\) is the inverse of the reduced Planck mass, \(m_{Pl}\) squared. Also the units are so chosen in which \(\hbar=c=1\).
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Mahmoodzadeh, A., Malekolkalami, B. Geodesics around oscillatons made of exponential scalar field potential. Astrophys Space Sci 363, 173 (2018). https://doi.org/10.1007/s10509-018-3389-8
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DOI: https://doi.org/10.1007/s10509-018-3389-8