Traversable wormholes in $f(R)$ gravity sourced by a cloud of strings

TL;DR

This paper investigates the construction and stability of traversable wormholes in $f(R)$ gravity with a cloud of strings as matter source, analyzing energy conditions, shape functions, and stability through numerical methods.

Contribution

It introduces a novel approach to formulating wormholes in $f(R)$ gravity using a string cloud, and compares their properties with wormholes supported by normal matter.

Findings

Wormholes with NEC violations are feasible in $f(R)$ gravity.

Wormhole solutions in the simple $f(R)$ model are found to be unstable.

The shape function can be constrained using geometrical and approximation methods.

Abstract

Wormhole solutions in General Relativity (GR) require \textit{exotic} matter sources that violate the null energy condition (NEC), and it is well known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in $f(R)$ modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the $rr$-component of the metric tensor, and employ Pad\`{e} approximation to check whether a well-constrained \textit{shape function} can be formulated in this manner. We then derive the field equations with a background of string cloud, and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple $f(R)$ gravity model, we use the background cloud of strings to estimate the wormhole shape function, and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple $f(R)$ gravity model considered. The results demonstrate that wormholes with NEC violations are feasible; however, the wormhole space-times in the simple $f(R)$ gravity model are unstable.