Cosmological Wormholes in General and Modified Theories of Gravity

Abstract

newline ABSTRACT newlineThe aim of this thesis is to explore the possible traversable wormhole geometries newlinebased on both general and modified theories of gravity. The thesis is newlinestructured into seven chapters, each addressing different aspects of wormhole newlinephysics. Chapter 1 introduces the basic terminology, reviews relevant literature, newlineprovides the rationale for the study, and offers a brief overview of wormhole newlinephysics. newlineIn Chapter 2, we study traversable wormholes in general relativity (GR) newlinewith a non-zero cosmological constant. We employ the Karmarkar condition to newlinecalculate the wormhole s shape function, which meets all of the necessary criteria newlinefor wormhole geometry, establishing a bridge between two distinct spacetimes. newlineWe also graphically analyze all energy conditions (ECs), anisotropic parameters, newlineand the cosmological constant s behavior. Furthermore, the chapter examines newlinethe stability of the obtained wormhole by using causality and Herrera-cracking newlinetechniques. The findings suggest that a traversable wormhole in GR with a newlinecosmological constant is possible in the presence of non-exotic matter (NEM). newlineIn Chapter 3, we present the possibility of traversable wormhole solution newlinewithin the Lyra manifold (LM) using the logarithmic shape function with constant newlineredshift function. We observe that the gravitational fluid violates the null newlineenergy condition (NEC) in GR, whereas all the ECs are satisfied in LM. The newlineviolation of NEC indicates the requirement of exotic matter (EM) in GR for the newlineconstruction of traversable wormholes, whereas LM supports NEM for the same newlinepurpose. Further, we analyze the stability of the wormhole using causality and newlineHerrera s cracking method and found that the obtained wormhole solution in the newlineLM is stable. newlineIn Chapter 4, the wormhole shape function is derived using the Karmarkar newlinecondition. This shape function joins two asymptotically flat spacetimes by satvi newlineisfying all the necessary requirements. The chapter uses graphical methods to newlineanalyze the behavior of the shape function, ECs, and anisotropic parameter. newlineFor examining stability of the solution, the causality and Herrera-cracking approaches newlineare used, which confirm the existence of a stable, traversable wormhole newlinesolution in LM using the Karmarkar condition. newlineIn Chapter 5, we investigate charged traversable wormhole solutions in LM. newlineTwo different types of shape functions with a constant redshift function are employed newlineto derive these solutions. The matter content consists of an anisotropic newlinefluid combined with an energy-momentum tensor (EMT) with charge. The chapter newlinederives exact wormhole solutions that satisfy all ECs, including null, weak, newlinestrong, and dominant ECs. It further analyzes the behavior of anisotropic parameters, newlinegauge functions, and other fundamental properties of the wormhole. newlineThe Tolman-Oppenheimer-Volkoff (TOV) equation is used to examine the stability newlineof these solutions, and the results show that the solutions meet the equilibrium newlinecondition, indicating the existence of viable and stable charged traversable newlinewormholes in LM supported by NEM. newlineIn Chapter 6, we derive traversable wormhole solutions in Barber s second newlineself-creation theory (BSSCT) for two different scenarios. In the first scenario, newlinewe use the relation pt = npr, where n is an arbitrary constant. In the second newlinescenario, we use a traceless EMT (which is usually associated with the casimir newlineeffect) along with the shape function b(r) = r2 newline0 newliner where r0 is the initial throat radius newlineto solve the field equations in this theory. In the first scenario, we determine newlinethat the ECs are violated, indicating the existence of a wormhole solution in the newlinepresence of EM. In the second scenario, we demonstrate that the wormhole solution newlinesatisfies the null, weak, strong, and dominated ECs, indicating the existence newlineof a traversable wormhole in BSSCT in the presence of NEM. In addition, we newlineuse the causality and Herrera cracking conditions to check the stability of the newlinevii newlineobtained wormhole solutions and discover that both the solutions are unstable. newlineFinally, in Chapter 7 discusses concluding remarks and future research directions newlinebased on the findings of the thesis. newlineKeywords: Traversable wormhole; Karmarkar condition; Cosmological constant; newlineGeneral relativity; Lyra manifold; Barber s second self-creation theory; newlineExotic matter; Non-exotic matter; Shape function; Redshift function; Embedded newlinediagram; Charged traversable wormhole; Energy conditions; Anisotropic parameter; newlineGauge function; Barber s scalar; d Alemberian operator; Energy-momentum newlinetensor; Stability analysis; TOV equation. newlineviii