Probing the existence of the ZTF Casimir wormholes in the framework of $f(\mathcal{R})$ gravity

TL;DR

This paper investigates the existence, energy conditions, and stability of Zero Tidal Forces Casimir wormholes within various $f( ext{R})$ gravity models, using analytical and numerical methods to explore their physical viability.

Contribution

It introduces new shape functions and stability analyses for Casimir wormholes in quadratic and power-law $f( ext{R})$ gravity theories, extending previous work on wormhole solutions.

Findings

Stable wormhole solutions are found under certain conditions.

Energy conditions are analyzed and partially satisfied in modified gravity.

Numerical solutions reveal the behavior of hydrodynamical and anisotropic forces.

Abstract

For the spherically symmetric static traversable wormholes, supported by the Casimir energy in $f(\mathcal{R})=\mathcal{R}+\alpha \mathcal{R}^2$ Quadratic, $f(\mathcal{R})=f_0 \mathcal{R}^n$ power-law Modified Gravity (MOG) theories we investigate energy conditions and dynamical stability of the wormhole solutions. Especially, we study Zero Tidal Forces (ZTF) Casimir WH's with anisotropic fluid located at the throat. By using the Casimir energy density and modified Einstein Field Equations (EFE's) we derived suitable shape functions for each modified gravity of our consideration. The stability of Casimir traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman-Oppenheimer-Voklov (MTOV) equation. Besides, we have numerically solved MTOV and derived hydrodynamical, anisotropic and extra forces, that is present due to the non-conserved stress-energy tensor. Moreover, other fundamental quantities, such as Volume Integral Quantifier and total gravitational energy were derived.