f(R) wormholes embedded in a pseudo--Euclidean space $E^{5}$

TL;DR

This paper investigates analytic wormhole solutions in $f(R)$ gravity, examining energy conditions, shape functions, and travel feasibility, with a focus on the role of specific gravity models and parameters.

Contribution

It introduces a novel approach to construct wormhole solutions in $f(R)$ gravity satisfying energy conditions and explores conditions for human travel.

Findings

Wormhole solutions satisfying energy conditions are found.

Shape functions are bounded by the Gronwall--Bellman function.

Conditions for human travel through wormholes are identified.

Abstract

This work is devoted to the study of analytic wormhole solutions within the framework of $f(R)$ gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair $\{\Phi(r), b(r)\}$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably $f(R)$ gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the $f(R)$ gravity model and its derivatives are playing a major role, specially in considering the violation of the non--existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall--Bellman shape function, where the red--shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored.