A topologically charged four-dimensional wormhole and the energy conditions

TL;DR

This paper analyzes a topologically charged traversable wormhole, demonstrating that its energy-momentum tensor satisfies key energy conditions and exploring how global monopole charge affects its curvature and physical properties.

Contribution

It introduces a novel topologically charged wormhole model with parameters and monopole charge, showing compliance with energy conditions and analyzing curvature effects.

Findings

Energy-momentum tensor satisfies WEC and NEC.

Global monopole charge influences curvature and physical quantities.

The wormhole model is consistent with physical energy conditions.

Abstract

In this research work, our primary focus revolves around the examination of a specific category of traversable wormholes known as topologically charged generalized Schwarzschild-Simpson-Visser-type wormhole, $ds^2=-\Big(1-\frac{2\,M}{\sqrt{x^2+b^2}}\Big)\,dt^2+\Big(1-\frac{2\,M}{\sqrt{x^2+b^2}}\Big)^{-1}\,\Big(\frac{dx^2}{\alpha^2}\Big)+(x^2+a^2)\,(d\theta^2+\sin^2 \theta\,d\phi^2)$. This wormhole is uniquely defined by a pair of key parameters (length scales $a$ and $b$), together with the global monopole charge $\alpha$. A noteworthy outcome of our investigation is the observation that the energy-momentum tensor associated with this wormhole complies with both the weak energy condition (WEC) and the null energy condition (NEC). Furthermore, incorporation of global monopole charge introduces a substantial influence on the curvature properties of wormhole space-time and various associated physical quantities derived from this geometry.