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

TL;DR

This paper analyzes the behavior of timelike geodesics and periapsis precession in the Fisher-Janis-Newman-Winicour-Wyman spacetime, revealing conditions for negative precession and providing analytical solutions for specific parameter values.

Contribution

It revisits previous results on geodesics in this spacetime, relaxes assumptions, and identifies the parameter range where negative periapsis precession occurs, including analytical solutions for special cases.

Findings

Negative periapsis precession occurs when $\gamma < 1/2$.

For $\gamma=1/2$, negative precession does not occur.

Analytical solutions are obtained for $\gamma=0,1/4,1/2$.

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 $\gamma=1/2$.