Investigations into separable geodesics and embedding diagrams for wormholes - Chen, Peng Hua (2015)
This thesis aims to find analytical solutions for geodesics (especially non-equatorial ones) of rotating traversable wormholes and study the features of such wormholes. We are motivated by Teo’s work which gives the canonical form of the metric for the rotating traversable wormholes and shows interesting features of such wormholes. But Teo did not give the analytical solutions for non-equatorial geodesics of such wormholes. We follow Carter’s approach using the Hamilton-Jacobi method to find the analytical solutions for the geodesics. However it turns out that the geodesics of such wormholes do not have analytical solutions in general. Instead, we construct a slowly rotating wormhole from the canonical form and solve it analytically. In addition, we study and compare the features of different wormholes, especially embedding diagrams, exotic matter and Carter constant for each of them.