Timelike Geodesics in Naked Singularity and Black Hole Spacetimes II

TL;DR

This paper analyzes particle orbits and perihelion precession in naked singularity and black hole spacetimes, revealing distinctive orbital properties and potential observational differences among these geometries.

Contribution

It derives and compares orbit equations and perihelion precession in BST, JNW, and Schwarzschild spacetimes, highlighting their unique orbital characteristics.

Findings

Perihelion precession in BST and Schwarzschild spacetimes is similar.

In JNW spacetime, perihelion precession is opposite to Schwarzschild.

Distinct effective potential features differentiate these spacetimes.

Abstract

We derive here the orbit equations of particles in naked singularity spacetimes, namely the Bertrand (BST) and Janis-Newman-Winicour (JNW) geometries, and for the Schwarzschild black hole. We plot the orbit equations and find the Perihelion precession of the orbits of particles in the BST and JNW spacetimes and compare these with the Schwarzschild black hole spacetime. We find and discuss different distinguishing properties in the effective potentials and orbits of particle in BST, JNW and Schwarzschild spacetimes, and the particle trajectories are shown for the matching of BST with an external Schwarzschild spacetime. We show that the nature of perihelion precession of orbits in BST and Schwarzschild spacetimes are similar, while in the JNW case the nature of perihelion precession of orbits is opposite to that of the Schwarzschild and BST spacetimes. Other interesting and important features of these orbits are pointed out.