Traversable wormholes with vanishing sound speed in $f(R)$ gravity

TL;DR

This paper derives stable traversable wormhole solutions in $f(R)$ gravity without exotic matter, using power-law models and shape functions, showing small deviations from General Relativity can produce stable wormholes.

Contribution

The paper introduces exact traversable wormhole solutions in $f(R)$ gravity with no exotic matter, utilizing novel shape function approaches and stability analysis.

Findings

Stable wormhole solutions are achievable in $f(R)$ gravity without exotic matter.

Power-law and Padé approximant models effectively characterize shape functions.

Small deviations from General Relativity yield stable wormhole geometries.

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 $b(r)/r\sim r^{-1-\beta}$. The second one adopts Pad\'e 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.