Axially symmetric wormholes

TL;DR

This paper presents an exact vacuum solution to Einstein's equations describing axially symmetric wormholes, analyzing their geometric and physical properties, and generating wormhole geometries through cut-and-paste methods.

Contribution

It introduces a new exact solution with parameters controlling topology and mass, and explores the detailed structure of the resulting wormholes.

Findings

The solution depends on three parameters: throat radius, mass-related parameter, and axial defect parameter.

Generated wormholes exhibit specific embedding and geodesic behaviors.

The analysis reveals the presence of trapped surfaces and detailed tidal force structures.

Abstract

In this work, we derive an exact vacuum solution to the Einstein field equations that depends on three constant parameters: the throat radius $r_0$, a parameter $q$, which is closely associated with the Komar mass, and a parameter $s$, which introduces axial topological defect while avoiding the emergence of conical singularities. We employ the cut-and-paste construction to generate wormhole geometries from this solution for $q \neq 0$. In addition, we perform a detailed analysis of the embedding diagrams, the wormhole throat, the occurrence and structure of trapped surfaces, the behavior of geodesics, the associated tidal forces, the Petrov algebraic classification, the Newman-Penrose spin coefficients, and the corresponding invariant conserved charges.