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

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.

11 pages, 7 figures

References in corpus (11)

• Disappearing cosmological constant in f(R) gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Modified-gravity wormholes without exotic matter
• Modified gravity models of dark energy
• Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition
• Wormholes in a viable f(T) gravity
• Brans wormholes
• No realistic wormholes from ghost-free scalar-tensor phantom dark energy
• Topologically non-trivial configurations in the 4d Einstein--nonlinear $\sigma$-model system

Cited by in corpus (1)

• Kuchowicz gravastars in the braneworld formalism