Static Wormhole Solutions and Noether Symmetry in Modified Gauss-Bonnet Gravity

TL;DR

This paper investigates static traversable wormholes within modified Gauss-Bonnet gravity using Noether symmetry, constructing specific models and analyzing their physical stability and energy conditions.

Contribution

It introduces three specific $f( ext{G})$ models and studies their viability and stability as traversable wormholes in modified gravity.

Findings

Quadratic and exponential models yield stable wormhole solutions.

Traversability is consistent with null energy conditions.

Physical stability is confirmed inside the wormhole throat.

Abstract

In this paper, we analyze static traversable wormholes via Noether symmetry technique in modified Gauss-Bonnet $f(\mathcal{G})$ theory of gravity (where $\mathcal{G}$ represents Gauss-Bonnet term). We assume isotropic matter configuration and spherically symmetric metric. We construct three $f(\mathcal{G})$ models, i.e, linear, quadratic and exponential forms and examine the consistency of these models. The traversable nature of wormhole solutions is discussed via null energy bound of the effective stress-energy tensor while physical behavior is studied through standard energy bounds of isotropic fluid. We also discuss the stability of these wormholes inside the wormhole throat and conclude the presence of traversable and physically stable wormholes for quadratic as well as exponential $f(\mathcal{G})$ models.