The Finslerian wormhole models

Farook Rahaman,Saibal Ray,A A Usmani,Ayan Banerjee,Nupur Paul,S S De

doi:10.1140/epjc/s10052-016-4066-0

Abstract

We present models of wormhole under the Finslerian structure of spacetime. This is a sequel of our previous work (Eur Phys J 75:564, 2015) where we constructed a toy model for compact stars based on the Finslerian spacetime geometry. In the present investigation, a wide variety of solutions are obtained that explore wormhole geometry by considering different choices for the form function and energy density. The solutions, like the previous work, are revealed to be physically interesting and viable models for the explanation of wormholes as far as the background theory and literature are concerned.

Highlights

Scientists have been trying to describe the wormhole structure in two ways: either modifying the Einstein theory or the matter distribution part
As a historical anecdote we note that Cartan [18] initiated the self-consistent Finsler geometry model in 1935
In the beginning of 1996, Vacuru [23,24] constructed relativistic models of the Finsler gravity in a self-consistent manner. He derived the Finsler gravity and locally anisotropic spinors in the low energy limits of superstring/supergravity theories with N -connection structure, the velocity type coordinates being treated as extra-dimensional ones

Summary

Introduction

Scientists have been trying to describe the wormhole structure in two ways: either modifying the Einstein theory or the matter distribution part. We shall study the wormhole solution in the context of Finsler [17] geometry, which is one of the alternatives of the general relativity. Vacaru et al [25–27] explained the so-called anholonomic frame deformation method (AFDM) by using Finsler geometry methods, which allows one to construct generic off-diagonal exact solutions in various modified gravity theories. In this direction, a numerous class of exact solutions for the Finsler modifications of black hole, black ellipsoid/torus/brane and string configurations, and locally anisotropic cosmological solutions have been developed for the so-called canonical d-connection and Cartan d-connections.

Basic equations based on the Formalism of Finsler geometry

Some models for wormholes

Specific shape function and redshift function

Discussion and Conclusion