Some aspects of Morris–Thorne wormhole in Scalar–Tensor theory

Abstract

In this work, we reach the equations of motion of Morris–Thorne wormhole geometry by means of the Einstein Field Equations and Klein–Gordon Equation of Scalar–Tensor Theory. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy–momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole (WH), in the zero redshift function situation, if the energy–momentum distribution of the universe is isotropic. In addition, we represent the conditions in order that the Null Energy Condition (NEC) is satisfied in the zero redshift function case, for anisotropic distribution. We also propose a special class of traversable WH shape functions. We will be calling the WHs corresponding to that class of functions as the Yukawa Type WHs. We expressed the NEC for those WHs particularly. Furthermore, we determine the radial and the transverse pressures in zero redshift function situation.