Description

The thesis consists of six chapters. The first chapter contains a brief discussion on wormhole. Particularly, how the hypothetical concept of wormhole arises from the Schwarzschild vacuum field solution of Einstein field equations and the non-traversable Schwarzschild wormhole from the Kruskal space-time diagram. After then, Morris and Thorne's traversable wormhole, energy conditions, and thin shell wormhole are discussed in a compact way. In chapter two several wormhole solutions for isotropic and anisotropic matter fields for Morris-Thorne line element in the framework of Einstein gravity with zero tidal forces and non-zero tidal forces are studied such that all geometric and traversability conditions are satisfied. Also, in addition, we discuss a way of finding the most general asymptotically flat wormhole solutions for isotropic matter with a solution. Again, to determine this, it is seen that the null energy condition is violated at the throat of the wormhole for satisfying positive energy density and flaring-out condition. Chapter three presents several possible asymptotically flat wormhole solutions with Morris-Thorne static spherically symmetric space-time in the background of non-conservative Rastall gravity. Here we have given six asymptotically flat wormhole solutions, out of that two correspond to non-zero tidal forces and four with zero tidal forces. To investigate the agegeometrical conditions, it is seen that in two wormhole solutions for Rastall gravity not only null energy condition is violated but also the matter satsatisfies the strong energy condition at the throat depending upon the suitable choice of Rastall parameter.