Can electro-magnetic field, anisotropic source and varying $\Lambda$ be sufficient to produce wormhole spacetime ?

TL;DR

This paper presents exact solutions to Einstein-Maxwell equations with a variable cosmological constant, showing that wormholes can theoretically exist with physically acceptable matter sources, including electromagnetic fields and anisotropic matter, without exotic matter.

Contribution

It introduces a class of wormhole solutions where a variable cosmological constant compensates for energy condition violations, avoiding the need for exotic matter.

Findings

Wormhole solutions with variable $\Lambda(r)$ are possible.

Energy conditions are satisfied outside the wormhole throat.

Physically acceptable matter sources can support wormhole structures.

Abstract

It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions [WEC or NEC]). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term $\Lambda$ to be space variable, viz., $\Lambda = \Lambda (r)$. The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.