Bound Timelike Geodesic Motions In Simpson-visser Spacetime

Black holes are the simplest objects predicted by Einstein's General Theory of Relativity.There is a singularity at the center of the black hole.The curvature of spacetime is infinite at this point,which leads to invalidation of General Relativity.SimpsonVisser spacetime is proposed to solve this problem by introducing Simpson-Visser scale length.Adjusting the scale length,such a spacetime can describe a regular black hole or a traversable wormhole respectively.Sagittarius A* is the closest supermassive black hole candidate to the Earth and an ideal testbed to theories of gravity and black hole models.The GRAVITY interferometer of the European Southern Observatory Very Large Telescope is currently the most advanced ground-based optical/near-infrared interference imaging instrument.One of its main scientific goals is to test the effects of General Relativity around Sagittarius A*.Therefore,the GRAVITY interferomter also has the potential to detect Simpson-Visser spacetime around Sagittarius A*.Geodesic bound orbital motions of timelike test particles in Simpson-Visser spacetime will be investigated for the first time.Marginally bound orbits and innermost stable circular orbits are two special types of bound orbits.If there is a timelike particle,its geodesic orbit starts at rest at infinity with zero velocity and has a specific amount of angular momentum so that it can eventually be trapped in an unstable circular orbit around the central object.Such a orbit is a marginally bound orbit.For a timelike particle,there exists a minimal radius permitting stable circular motions around the central object.The circular orbits corresponding to such a radius are called innermost stable circular orbits.The energy and angular momentum ranges of bound orbits are determined by marginal bound orbits and innermost stable circular orbits.The bound orbits can be classified into precession orbits and periodic orbits.The precession orbits of timelike test particles in Simpson-Visser spacetime are obtained respectively in Newtonian limit,semi-classical approximation and relativistic situation.Based on the Solar System dynamics and the detected precession of the star S2 around the Galactic Center,a preliminary bound on the Simpson-Visser scale length is found.Perihelion precession of Mercury is one of the classical tests of General Relativity and the Schwarzchild precession of the star S2 has been detected by GRAVITY as well.There is no precession in the Newtonian limit,which is consistent with the result under Newtonian gravity.In the semi-classical approximation,the direction of precession is opposite to that of revolution,which is in conflict with the post-Newtonian precession in General Relativity.With the current accuracy,the orbital precessions of the Solar System planets can't provide a good constrain on the SimpsonVisser scale length,while the Schwarzchild precession of the star S2 measured by GRAVITY can give a preliminary constrain on such a scale length.The periodic orbits of timelike test particles in a strong gravitational field in Simpson-Visser spacetime are studied.It is found that the variation of the scale length can cause the transition between different periodic orbits.Three integers are used to describe the geometric properties of periodic orbits,which are the number of apoastrons,the number of extra whirls around the central object and the number of vertices between a certain apoastron and the successive one.In Simpson-Visser spacetime,the geometric properties of periodic orbits are determined by the energy and angular momentum of the test partcle and the Simpson-Visser scale length.The rotation and charge of the central object in Simpson-Visser specetime are not considered in this work,the effect of gravitational radiation is not taken into account neither.These effects will be investigated in further research.In future,the accumulation of GRAVITY observation on star S2 and the improvement of accuracy will provide a stricter constrain on Simpson-Visser scale length,which is helpful to the probe of Simpson-Visser spacetime.