Traversable wormholes with multiple unstable critical curves

Abstract

The number and position of unstable critical curves, as well as the nature of the accretion disk around compact objects, play a fundamental role in their optical appearance. Identifying differences in the optical spectrum of various observed compact objects can help classify them as black holes or black hole mimickers, such as traversable wormholes. Although multiple unstable critical curves have been reported to appear in asymmetric traversable wormholes, in this work we construct symmetric traversable wormholes with multiple unstable critical curves. We propose a general rational redshift function that allows us to trace the number of critical points of the effective potential and determine their nature as maxima or minima. The ray tracing method is used to study the trajectories of massless particles, particularly their behavior near the unstable critical points. Finally, a thin accretion disk model is implemented to analyze the optical appearance of the solution.