Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions

Abdul Jawad,Shamaila Rani

doi:10.1140/epjc/s10052-016-4560-4

Abstract

We explore wormhole solutions in a non-minimal torsion-matter coupled gravity by taking an explicit non-minimal coupling between the matter Lagrangian density and an arbitrary function of torsion scalar. This coupling depicts the transfer of energy and momentum between matter and torsion scalar terms. The violation of null energy condition occurred through effective energy-momentum tensor incorporating the torsion-matter non-minimal coupling while normal matter is responsible for supporting the respective wormhole geometries. We consider energy density in the form of non-monotonically decreasing function along with two types of models. First model is analogous to curvature-matter coupling scenario, that is, torsion scalar with $T$-matter coupling while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying null energy condition. Also, we find that the increasing value of coupling constant minimizes or vanishes the violation of null energy condition through matter.

Highlights

In order to find some realistic sources that support the wormhole geometry or minimize the usage of exotic matter, different varieties of wormhole solutions are explored
Our concentration goes toward modified theories of gravity where the effective scenario gives the violation of the null energy condition and the matter source supports the wormholes
In order to keep the throat open, the exotic matter is used, which violates the null energy condition and we elaborated the wormhole trajectories as hypothetical paths

Summary

Introduction

In order to find some realistic sources that support the wormhole geometry or minimize the usage of exotic matter, different varieties of wormhole solutions are explored. Sharif and Rani explored the wormhole solutions in this gravity taking a noncommutative background with a Gaussian distribution [49], dynamical wormhole solutions [50], for the traceless fluid [51], with the inclusion of charge [52] and galactic halo scenario [53] They considered some power-law f (T ) functions for which the effective energymomentum tensor depending on torsion contributed terms violating the null energy condition. Harko et al [58] introduced the most general conditions in the framework of modified gravity, that is, the matter threading the wormhole throat satisfies all of the energy conditions, while the gravitational fluid (such as higher order curvature terms) supports the nonstandard wormhole geometries.

Non-minimal Torsion–matter Coupling

Gravitational field equations for wormhole geometry

Wormhole solutions

Model 1

Model 2

Concluding remarks