Timelike geodesics in Naked Singularity and Black Hole Spacetimes

TL;DR

This paper analyzes timelike geodesics in naked singularity and black hole spacetimes, deriving orbit solutions and comparing orbital properties, revealing unique precession behaviors that distinguish these spacetimes.

Contribution

It provides the first detailed comparison of particle orbits in naked singularity versus black hole spacetimes, highlighting novel orbital precession phenomena.

Findings

Naked singularity orbits can precess opposite to particle motion.

Distinct orbital precession patterns differentiate naked singularities from black holes.

Particle bound orbits exhibit unique precession behaviors in naked singularity spacetimes.

Abstract

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. The Schwarzschild and naked singularity spacetimes considered here can be formed as end state of a spherically symmetric gravitational collapse of a matter cloud. We find and compare the perihelion precession of the particle orbits in the naked singularity spacetime with that of the Schwarzschild black hole. We then discuss different distinguishable physical properties of timelike orbits in the black hole and naked singularity spacetimes and implications are discussed. Several interesting differences follow 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.