Wormhole Geometry and Noether Symmetry in f(R) Gravity

TL;DR

This study explores the geometry and stability of traversable wormholes in $f(R)$ gravity using Noether symmetry, analyzing different models and conditions to identify physically viable solutions.

Contribution

It introduces a Noether symmetry approach to find and analyze wormhole solutions in various $f(R)$ gravity models, including stability and energy condition assessments.

Findings

Wormhole solutions are physically viable and traversable in all models analyzed.

Most constructed wormholes are found to be stable.

Graphical analysis confirms the satisfaction of energy conditions for these solutions.

Abstract

This paper investigates the geometry of static traversable wormhole through Noether symmetry approach in $f(R)$ gravity. We take perfect fluid distribution and formulate symmetry generators with associated conserved quantities corresponding to general form, power-law and exponential $f(R)$ models. In each case, we evaluate wormhole solutions using constant and variable red-shift functions. We analyze the behavior of shape function, viability of constructed $f(R)$ model and stability of wormhole solutions graphically. The physical existence of wormhole solutions can be examined through null/weak energy conditions of perfect fluid and null energy condition of the effective energy-momentum tensor. The graphical interpretation of constructed wormhole solutions ensures the existence of physically viable and traversable wormholes for all models. It is concluded that the constructed wormholes are found to be stable in most of the cases.