Abstract
We derive exact traversable wormhole solutions in the framework of f(R) gravity with no exotic matter and with stable conditions over the geometric fluid entering the throat. For this purpose, we propose power-law f(R) models and two possible approaches for the shape function b(r)/r. The first approach makes use of an inverse power-law function, namely b(r)/rsim r^{-1-beta }. The second one adopts Padé approximants, used to characterize the shape function in a model-independent way. We single out the P(0, 1) approximant where the fluid perturbations are negligible within the throat, if the sound speed vanishes at r=r_0. The former guarantees an overall stability of the geometrical fluid into the wormhole. Finally, we get suitable bounds over the parameters of the model for the above discussed cases. In conclusion, we find that small deviations from general relativity give stable solutions.
Highlights
If the Birkhoff theorem is valid and matter fields are included in a non-vanishing energy–momentum tensor, this approach leads to severe bounds at the wormhole throat
The throat is assumed as an inverse power of the radial coordinate
We introduce the basic ingredients of our approach
Summary
We can state that: Stable and traversable wormhole solutions are possible for small deviations of Einstein’s gravity in the presence of standard perfect fluid matter. These results allow to give necessary conditions on the function b(r )/r but they are not sufficient to show that the form of b(r ) is of the form of a polynomial To ensure this hypothesis, we assume that the sound speed, i.e., the variation of the pressure with respect to the density is negligibly small [38]. We assume that the sound speed, i.e., the variation of the pressure with respect to the density is negligibly small [38] Combining this additional requirement, we stabilize the solution as we shall show below
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