Traversable wormhole geometries in $f(Q)$ gravity

TL;DR

This paper explores traversable wormhole solutions within $f(Q)$ gravity, analyzing their stability, energy conditions, and geometric properties across various models and shape functions.

Contribution

It introduces new wormhole geometries in $f(Q)$ gravity considering different assumptions, and assesses their stability and physical viability.

Findings

NEC violation in all wormhole models

Wormholes are found to be stable under certain conditions

Embedding diagrams illustrate the wormhole structures

Abstract

The current interests in the universe motivate us to go beyond Einstein's General theory of relativity. One of the interesting proposals comes from a new class of teleparallel gravity named symmetric teleparallel gravity, i.e., $f(Q)$ gravity, where the non-metricity term $Q$ is accountable for fundamental interaction. These alternative modified theories of gravity's vital role are to deal with the recent interests and to present a realistic cosmological model. This manuscript's main objective is to study the traversable wormhole geometries in $f(Q)$ gravity. We construct the wormhole geometries for three cases: (i) by assuming a relation between the radial and lateral pressure, (ii) considering phantom energy equation of state (EoS), and (iii) for a specific shape function in the fundamental interaction of gravity (i.e. for linear form of $f(Q)$). Besides, we discuss two wormhole geometries for a general case of $f(Q)$ with two specific shape functions. Then, we discuss the viability of shape functions and the stability analysis of the wormhole solutions for each case. We have found that the null energy condition (NEC) violates each wormhole model which concluded that our outcomes are realistic and stable. Finally, we discuss the embedding diagrams and volume integral quantifier to have a complete view of wormhole geometries.