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.
Highlights
Equation (20) involves term f R = d f /d R, as we consider violation of non-existence theorem (i.e., d f /d R < 0) for spherically symmetric wormhole structure, for ρ + pt > 0 the remaining term should be negative. This examination shows the importance of flaring out condition and selection of f (R) gravity model
For R∗ > 0 and μ > 0, we found that the existence of exotic matter can be avoided at the throat for the traversable wormhole geometry
For the combinations R∗ < 0, μc > 0 and R∗ > 0, μc > 0, we found that F < 0 and weak energy condition (WEC) is at the throat
Summary
Morris–Thorne [11] were the first who gave the idea that human being can travel through wormhole tunnels. Different researchers discussed wormholes geometry in different modified theories of gravity [13,14,15,16,17,18,19]. In 1970, Buchdahl [20] proposed one of the most well known and simplest modified theory of gravity i.e., f (R) gravity which can be obtained by adopting a modification in the Einstein Hilbert action with an arbitrary function of the Ricci scalar R Following in this way, several modifications of GR have been developed by considering different approaches. Discussed static spherically symmetric wormholes with nonexotic matter (respected energy conditions) in the framework of f (R) gravity. Fayyaz and Shamir [44] constructed a WSF by applying KMc and analysed that it obeys all the required conditions and exhibit the presence of exotic matter in the context of GR.
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