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

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 $$\tilde{L}$$ 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.

Geodesic motion in Euclidean Schwarzschild geometry

“… The detailed investigation of geodesic motion in the case of Lorentzian signature of the metric performed in Refs. [ 3 – 6 ], as well as the more recent works regarding Schwarzschild–(anti-)de Sitter spacetimes, BTZ black holes, noncommutative Schwarzschild black holes, and static and spherically symmetric traversable wormholes geometries [ 7 – 10 ]. The proof in Ref.…”