Bound orbits in a class of traversable wormhole spacetimes

Abstract

We consider a two-parameter family of spherically-symmetric wormhole spacetimes introduced by Konoplya and Zhidenko. Such wormholes belong to the more general Morris-Thorne class of traversable wormholes. We study timelike geodesics in this class of spacetimes and investigate the possibility of bound orbits. For Konoplya-Zhidenko wormholes, we show that there exists only an unstable circular orbit at the throat location. This particular class of wormhole spacetimes also admits eccentric bound orbits for a particular set of initial conditions (particle energy, initial radial position, wormhole throat and shape exponent, and the parameter p). We generalized our result to the generic Morris-Thorne class of traversable wormholes and demonstrated that this class does not permit stable circular orbit at the throat.