Finite mass two throat wormholes: global light rings, branch resolved strong lensing, and scalar transmission

Abstract

We introduce a static, horizonless, asymptotically flat two throat wormhole family in which one global metric determines the geometry, effective source, null dynamics, lensing, and test field propagation. A finite mass deformation of a quartic embedding profile produces two symmetric throats and an intermediate equator, while the associated Misner--Sharp mass tends to the same finite value at both asymptotic ends. The temporal sector yields the same mass parameter, and the Einstein tensor defines a single conserved anisotropic source. In addition to the local flare out identity, the complete radial averaged null functional is obtained exactly and is strictly negative. The global null potential admits a complete phase classification for all positive masses and nonnegative redshift deformation. Depending on the parameters, the global unstable set consists of throat rings, four off throat rings, or exterior rings accompanied by a subcritical equatorial ring. In the four ring phase, all unstable rings have the same impact scale but the inner and outer branches have different Lyapunov exponents. We derive the logarithmic strong deflection coefficients analytically and show that the cross throat coefficient is the sum of the contributions from every global maximum traversed by the ray. Direct numerical integration verifies these coefficients. The scalar scattering problem exhibits phase dependent barriers and resonant transmission. The resulting model provides a finite mass setting in which topology, averaged energy conditions, branch resolved strong lensing, and wave transmission are derived from one spacetime.