Exploring The Existence Of Non-Commutative Wormhol

Abstract

Scalar tensor theories appear as handy candidate to analyze the stellar objects like compact stars and wormholes. In this thesis, we have discussed about the non commutative spherically symmetric wormhole solutions in f(R,Φ) gravity. Forthispurpose,weconsidertwodifferentframeworkssuchasGaussiandistribution as well as Lorentzian distribution non commutative geometry. With the help of Gaussian and Lorentzian distribution we have found the exact and numericalsolutionsofthenoncommutativewormhole’sinf(R,Φ)gravity. Byconsidering suitable values of the unknown parameters, we analyse the different characteristics of the wormhole’s models analytically as well as graphically.It has been observed that without involving any exotic material it is feasible to acquire wormhole’s solution in this theory.For this purpose firstly we consideredthedifferentcategoriesoffluidsi.eanisotropic,anisotropicandbarotropic fluids. For all these fluids we analyzed the energy conditions to examine the f(R,Φ) gravity. To check the energy conditions we have calculated b(r) numerically as well as graphically in order to check whether the wormhole solutions exist or not. It has been concluded that the solution we obtained is idealistic. We have also analyzed the energy conditions (NEC and WEC) in detail. We have concluded that for the existence of non commutative wormhole’s solution theseenergyconditionsarevalid. Andalsoforthesecases,weobservedthatfor anisotropic fluid, realistic wormhole geometries can be constructed that satisfy the energy conditions. We find the shape function which protects the worm hole throat and enables us to discuss the requirement of exotic matter. We also analyze the energy constraints using the graphical schemes.