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Classification Of Topological Defects In Cosmological Models, Abigail Swanson
Classification Of Topological Defects In Cosmological Models, Abigail Swanson
Student Research Submissions
In nature, symmetries play an extremely significant role. Understanding the symmetries of a system can tell us important information and help us make predictions. However, these symmetries can break and form a new type of symmetry in the system. Most notably, this occurs when the system goes through a phase transition. Sometimes, a symmetry can break and produce a tear, known as a topological defect, in the system. These defects cannot be removed through a continuous transformation and can have major consequences on the system as a whole. It is helpful to know what type of defect is produced when …
Einstein's Equations, Lagrangians For General Relativity, And Adm Formalism, Timothy Corbett
Einstein's Equations, Lagrangians For General Relativity, And Adm Formalism, Timothy Corbett
Student Research Submissions
Einstein’s equations describe the relation of spacetime curvature and present matter. We will consider the case of a Lorentzian manifold diffeomorphic to ℝ × Σ, where time t ∈ ℝ and the three-dimensional manifold Σ represents space. In a homogeneous and isotropic universe, the three-dimensional manifold Σ of the Lorentzian manifold has Riemann curvature tensor (3)R = KI, where K is a constant and I is the 3 × 3 identity matrix. Space is flat when K = 0, spherical when K is positive, and hyperbolic when K is negative. In this paper, we will show models agreeing with …