Timelike geodesics in naked singularity and black hole spacetimes

In this paper, we derive the solutions of orbit equations for a class of naked singularity spacetimes and compare these with timelike orbits, that is, particle trajectories in the Schwarzschild black hole spacetime. We find and compare the perihelion precession of particle orbits in the naked singularity spacetimes with that of a Schwarzschild black hole. We then discuss different distinguishable physical properties of timelike orbits in the black hole and naked singularity geometries, and implications are discussed. Several interesting differences emerge from our results, including the conclusion that in naked singularity spacetimes particle bound orbits can precess in the opposite direction of particle motion, which is not possible in Schwarzschild spacetime. Such reverse precession and other distinctions may help distinguish a naked singularity from a black hole observationally.

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