Catenoid Inspired Hyperbolic Wormhole Geometry

TL;DR

This paper introduces a new class of traversable, finite, spherically symmetric wormholes inspired by catenoid minimal surfaces, analyzing their geometry, energy conditions, traversability, and stability.

Contribution

It presents a novel catenoid-inspired wormhole geometry with detailed curvature analysis, energy condition assessment, and stability considerations, expanding theoretical models of traversable wormholes.

Findings

Wormholes are supported by anisotropic exotic matter.

The geometry is finite and bounded in spatial extent.

The analysis confirms traversability and stability under certain conditions.

Abstract

We unveil a novel class of traversable wormholes exhibiting exact spherical symmetry, geometrically inspired by the minimal surface structure of a catenoid. Introducing the spacetime metric, we rigorously derive its fundamental curvature properties, including the Riemann curvature tensor, and consequently compute the Einstein tensor and stress-energy tensor. This framework reveals that the wormhole is sustained by an anisotropic fluid. A detailed analysis of the energy conditions demonstrates the requisite presence of exotic matter, establishing the physical viability and constraints of this configuration. Subsequent investigations address the wormhole's traversability characteristics, gravitational lensing signatures, and dynamic stability. Crucially, we establish that this catenoid-inspired spacetime represents a finite wormhole, possessing bounded spatial extent.