Dynamics in wormhole spacetimes: a Jacobi metric approach

Abstract

This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris–Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole background. Finally, we discuss about the restrictions over the stress–energy tensor imposed by the existence of elliptic orbits in the Kepler problem.

The generalized Jacobi metric

“…The previous result is in agreement with the Jacobi metric 4 obtained in [3]. Moreover, we were able to reproduce the results obtained in [6]. In the following section we show the results obtained for stationary axi-symetric spacetimes, then we particularize for Kerr spacetime.…”

“…Until now, the known Jacobi metric worked very well for static, spherically symmetric asymptotically flat spacetimes [2,3]. The method has been widely used for studying the dynamics of particles moving in those spacetimes by using the tools of Riemannian geometry [7,5,6]. However, the method has some difficulties when applied to stationary spacetimes .…”

“…The Kerr metric has two killing vectors ∂ t and ∂ φ commuting with each other. Both of them satisfy the killing equation 6 . As we have seen before, for stationary spacetimes the energy E and angular momenta L are linear combinations of ṫ and φ…”

“…The extension to time dependent and stationary metrics were studied in [3,4]. The formalism was also applied to charged black holes [5] and wormholes [6]. The formalism worked well when dealing with static, spherically symmetric, asymptotically flat spacetimes and with time dependent asymptotically flat metrics.…”

Spinning test particle motion around a rotating wormhole

“…The idea of wormholes has been considered in different scenarios, such as Einstein's gravity [21][22][23][24][25][26][27][28][29][30][31] and alternatives theories of gravity [32][33][34][35][36]. In Ref.…”