Axially symmetric wormholes

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.

Figures (8)

• Figure 1: Shape curve and its corresponding surface of revolution with $\ell = 2$.
• Figure 2: Shape curve and its corresponding surface of revolution with $\ell \to \infty$.
• Figure 3: Shape curves for the sphere and for surfaces with $\ell = 1.001$ and $\ell = 100.0$.
• Figure 4: Profile curve and embedding surface of the wormhole with $q = 2$, $r_0 = 1$ and $\theta = \tfrac{\pi}{2}$.
• Figure 5: Graphs of $V_{eff} (r)$ for three values of the impact parameter $b$: $b_c - 0.03$, $b_c$ and $b_c + 0.03$. To plot them, we set $q = 2$, $r_0 = 1$ and $\theta = \tfrac{\pi}{2}$.