Asymmetric Thin-Shell Wormhole

Wormholes appeared in general relativity as special solutions to Einstein’s field equations. These bizarre structures can be visualized as tunnels connecting remote points within a single spacetime or points of two distinct spacetimes. The main problem with the wormholes is that they are supported by exotic matter; a kind of matter which does not satisfy the known energy conditions. In 1988, Morris and Thorne published a paper and discussed the traversability of wormholes. The paper soon came to researchers’ focus and caused a new wave of studies over structural characteristics of wormholes. In 1989, in one of these attempts, Visser developed a method with which a new class of traversable wormholes came into existence; thin-shell wormholes. The principal aim was to tackle with the exotic matter that necessarily gave life to such objects. Visser’s recipe was to confine the exotic matter to a very narrow surface, i.e. the throat of the thin-shell wormhole so that its existence can be justified in some way. Thinshell wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the throat. This gives rise to an asymmetric thin-shell wormhole, whose mechanical stability is studied here in the framework of the linear stability analysis. In the first half of this dissertation, having constructed a general formulation, using barotropic and variable equations of state, also related junction conditions, the results are closely studied for some examples of diverse geometries in general relativity. Specifically, the role of asymmetry in the stability of thin-shell wormholes, if any, has been studied. It is shown that the stability of such peculiar objects can be studied in the context of linear stability analysis and that they can be mechanically stable. It is seen that the asymmetric structures of thin-shell wormholes are less likely to be stable compared with their symmetric counterparts. Also, it is shown that the discontinuities which appear in the stability diagrams of the asymmetric thin-shell wormholes are due to a flaw in the barotropic equation of state, and that such discontinuities can be lifted by exploiting a radius-dependent variable equation of state. The second half is devoted to constructing static thin-shell wormholes in new massive gravity and investigating their properties. It is shown that the asymmetry arises naturally in these thin-shell wormholes. Additionally, solutions such as static BTZ and new type black holes, and warped (A)dS3 solutions admit no thin-shell wormholes. Finally, the energy density and pressure of the constructed asymmetric thin-shell wormholes become zero which implies no exotic matter. Keywords: Thin-Shell Wormhole, Thin-Shell Formalism, General Relativity, New Massive Gravity, Exotic Matter, Asymmetry.