Wormhole Geometry and Noether Symmetry in f(R) Gravity

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.

33 pages, 18 figures, to appear in Annals of Physics

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• Wormholes in 4D Einstein-Gauss-Bonnet Gravity
• Gravitational lensing by wormholes supported by electromagnetic, scalar, and quantum effects
• Conformally symmetric traversable wormholes in modified teleparallel gravity
• Evolving topologically deformed wormholes supported in the dark matter halo
• Charged Wormhole Solutions in Einstein-Cartan gravity
• Charged traversable wormholes supported by Casimir energy with and without GUP corrections
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• Existence of Wormholes in $f(\mathcal{G})$ Gravity using Symmetries
• A topologically charged four-dimensional wormhole and the energy conditions
• f(R) wormholes embedded in a pseudo--Euclidean space $E^5$
• Novel Casimir wormholes in Einstein gravity
• Viable Wormhole Structures and Energy Conditions in f(Q,T) Theory
• Wormhole solutions in generalized Rastall gravity
• Casimir Wormholes in Brans-Dicke Theory
• Trace anomaly contributions to semi-classical wormhole geometries