Circular Orbits and Photon Orbits at Wormhole Throats

In this work we study timelike circular orbits and photon orbits at the throat of stationary and axisymmetric wormholes. Our minimal requirements on the spacetime are the existence of a global radial coordinate l, which connects both sides of the wormhole, two times differentiable metric components with respect to l at the wormhole throat and vanishing first derivatives of the metric components at the wormhole throat, which is the case for symmetrical wormholes. We derive expressions in terms of the metric components for the specific angular momentum $\ell$ of a test particle, that describe a possible spectrum of solutions for bound circular orbits at the wormhole throat. We identify a phase transition in the parameter space, which occurs if an ergoregion is present. Furthermore, we showcase expressions for the parameter space in terms of physical properties of the spacetime in the form of the throat circumference $C_T$ , the angular frequency of the wormhole $\omega$ and the gravitational redshift $z$. An analysis of these expressions and the characteristics of the photon orbits gives constraints on wormhole properties, as it hints to possible instabilities, such as for fast rotating wormholes and wormholes with an ergoregion. Through the use of accretion disk models, the existence of possible stable circular orbits could be linked to accretion disks surrounding the wormhole throat.