Conformally symmetric traversable wormholes in modified teleparallel gravity

TL;DR

This paper explores traversable wormhole solutions within teleparallel gravity frameworks, deriving exact solutions under conformal symmetry, analyzing energy conditions, and examining various matter configurations and models.

Contribution

It provides new analytical wormhole solutions in TEGR and $f(T)$ gravity, incorporating conformal symmetry constraints and diverse matter equations of state.

Findings

Wormholes violate weak and null energy conditions at the throat.

Exact solutions are obtained under conformal symmetry assumptions.

Energy conditions are analyzed for power-law $f(T)$ models.

Abstract

In this paper, we consider wormhole geometries in the context of teleparallel equivalent of general relativity (TEGR) as well as $f(T)$ gravity. The TEGR is an alternative geometrical formulation of Einstein's general relativity, where modified teleparallel gravity or $f(T)$ gravity has been invoked as an alternative approach for explaining an accelerated expansion of the universe. We present the analytical solutions under the assumption of spherical symmetry and the existence of a conformal Killing vectors to proceed a more systematic approach in searching for exact wormhole solutions. More preciously, the existence of a conformal symmetry places restrictions on the model. Considering the field equations with a diagonal tetrad and anisotropic distribution of the fluid, we study the properties of traversable wormholes in TEGR that violates the weak and the null energy conditions at the throat and its vicinity. In the second part, wormhole solutions are constructed in the framework of $f(T)$ gravity, where $T$ represents torsion scalar. As a consistency check, we also discuss the behavior of energy conditions with a viable power-law $f(T)$ model and the corresponding shape functions. In addition, a wide variety of solutions are deduced by considering a linear equation of state relating the density and pressure, for the isotropic and anisotropic pressure, independently of the shape functions, and various phantom wormhole geometries are explored.