Time-Dependent Wormhole Solutions of $f(R)$ Theory of Gravity and Energy Conditions

TL;DR

This paper constructs time-dependent wormhole solutions within $f(R)$ gravity, demonstrating that the matter supporting these wormholes can satisfy energy conditions during different expansion phases.

Contribution

It introduces exact $f(R)$ wormhole solutions with specific shape functions and expansion laws, analyzing their energy condition compliance.

Findings

Wormhole solutions satisfy NEC and WEC during accelerated expansion

Solutions are derived for traceless matter with specific shape functions

Exact solutions are obtained for power-law expansion scenarios

Abstract

In this work, we construct time-dependent wormhole solutions in the context of $f(R)$ theory of gravity. The background matter is considered to be traceless. By considering specific shape function and power-law expansion exact solutions for $f(R)$ are found. The null and the weak energy conditions (NEC and WEC) are checked for wormhole solutions. It is shown that the matter threading the wormhole spacetimes with either accelerated expansion or decelerated expansion satisfies the NEC and WEC.