Traversable Wormhole Solutions in $f(R)$ Gravity Via Karmarkar Condition

TL;DR

This paper constructs a new wormhole shape function using the Karmarkar condition within $f(R)$ gravity, demonstrating solutions that require minimal exotic matter and are potentially stable, advancing analytical models of wormholes in modified gravity theories.

Contribution

It introduces a novel shape function for traversable wormholes in $f(R)$ gravity that minimizes exotic matter and ensures stability, expanding analytical solutions in modified gravity.

Findings

The shape function connects two asymptotically flat regions.

Wormhole solutions require less exotic matter with appropriate $f(R)$ models.

Solutions are stable and analytically representable in $f(R)$ gravity.

Abstract

Motivated by recent proposals of possible wormhole shape functions, we construct a wormhole shape function by employing the Karmarkar condition for static traversable wormhole geometry. The proposed shape function generates wormhole geometry that connects two asymptotically flat regions of spacetime and satisfies the required conditions. Further, we discuss the embedding diagram in three-dimensional Euclidean space to present the wormhole configurations. The main feature of current study is to consider three well-known $f(R)$ gravity models, namely exponential gravity model, Starobinsky gravity Model and Tsujikawa $f(R)$ gravity model. Moreover, we investigate that our proposed shape function provides the wormhole solutions with less (or may be negligible) amount of exotic matter corresponding to the appropriate choice of $f(R)$ gravity models and suitable values of free parameters. Interestingly, the solutions obtained for this shape function generate stable static spherically symmetric wormhole structure in the context of non-existence theorem in $f(R)$ gravity. This may lead to a better analytical representation of wormhole solutions in other modified gravities for the suggested shape function.