Stability analysis of circular orbits around a traversable wormhole with massless conformally coupled scalar field

TL;DR

This paper analyzes the stability of circular orbits around a traversable wormhole solution in Einstein's gravity coupled with a massless scalar field, using Lyapunov stability to classify orbit stability.

Contribution

It provides a detailed stability analysis of timelike and null circular orbits around a specific wormhole spacetime using Lyapunov methods.

Findings

Timelike orbits exhibit four types of effective potentials based on angular momentum.

Null geodesics have effective potential with only centrifugal component.

Circular orbits are classified into stable and unstable based on Lyapunov stability analysis.

Abstract

We study the stability of circular orbits in the background of a traversable wormhole (TWH) spacetime obtained as a solution of Einstein's field equations coupled conformally to a massless scalar field. The Lyapunov stability approach is employed to determine the stability of circular orbits (timelike and null) of non-spinning test particles around a TWH spacetime. In the case of timelike geodesics, the particle is confined to move in four different types of effective potentials depending on various values of the angular momentum L with both centrifugal and gravitational part. The effective potential for null geodesics consists of only a centrifugal part. Further, we characterize each fixed point according to its Lyapunov stability, and thus classify the circular orbits at the fixed point into stable center and unstable saddle points by depicting the corresponding phase-portraits.