Conformally symmetric traversable wormholes

TL;DR

This paper derives a variety of exact traversable wormhole solutions under conformal symmetry, exploring their matter distributions, energy conditions, and traversability constraints, including asymptotically flat cases and minimal exotic matter requirements.

Contribution

It introduces a systematic method for finding exact wormhole solutions with conformal symmetry, including novel geometries with restricted exotic matter and minimal energy condition violations.

Findings

Many solutions have exotic matter confined near the throat.

Asymptotically flat solutions are obtained.

Minimal amounts of energy condition violating matter are sufficient.

Abstract

Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a {\it non-static} conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cut-off of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the ``volume integral quantifier,'' it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.