The existence of massive particle surfaces can be inferred from the constancy of the quotient between energy and mass, the so called master equation. In this article we present a study of the massive particle surfaces of traversable wormholes. We use a purely a geometric approach based in the curvatures of a 2-dimensional Riemannian metric obtained by projecting the spacetime metric over surfaces of constant energy. Using the asymptotic and near throat limits of geodesic curvature, together with the sign of the Gaussian curvature we are able to determine the existence of LR’s and TCO’s and analyze its stability. We show that the general definition of a wormhole throat, namely the characterization of the throat in terms of a 2–dimensional constant-time hypersurface of minimal area, is equivalent to the conditions over the geodesic and Gaussian curvature, allowing for a general definition of a wormhole throat. We analyze in detail the Morris-Thorne family of wormholes and the Damour-Solodukhin wormholes. In the first case there is not a massive particle surface, while in the second there are more than one place where it can form. We show that for the wormholes considered there is always an odd number of light rings, one of them at the throat. In the case of Morris-Thorne wormhole our method leads to a procedure for building a wormhole with more than one LR. We study how the procedure can be extended to other wormhole spacetimes.
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