Revisiting timelike geodesics in the Fisher-Janis-Newman-Winicour-Wyman spacetime

Abstract

We investigate the timelike geodesics and the periapsis precession of orbits in the Fisher-Janis-Newman-Winicour-Wyman spacetime. This spacetime represents the naked singularity spacetime in the Einstein-massless scalar system. We revisit the results in the previous studies and relax the assumptions about the eccentricity of a bound orbit and the size of a semilatus. We find that the negative periapsis precession occurs when the spacetime sufficiently deviates from the Schwarzschild spacetime. In particular, for the small eccentric orbits, we show the negative periapsis precession occurs for $\gamma <1/2$, where $\gamma$ is the deviation parameter from the Schwarzschild spacetime. We also obtain the analytical solutions for the special cases of $\gamma =0,1/2,1/4$. Then, we show that the negative precession never occurs for $\gamma =1/2$.

26 pages, 7 figures

References in corpus (4)

• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Towards an observational test of black hole versus naked singularity at the galactic center
• Geodesic structure of Janis-Newman-Winicour space-time

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• Nonspherically-symmetric black hole in Einstein-massless scalar theory
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• Extended mass and spheroidal deformation effects on epicyclic frequencies and periapsis shift in quasi-circular orbits