Date of Award
Bachelor of Science
Department Chair or Program Director
Major or Concentration
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 each. We will derive the Schwarzschild metric, find Einstein’s equations from the Lagrangian, and analyze them using Arnowitt-Deser-Misner formalism.
Corbett, Timothy, "Einstein's Equations, Lagrangians for General Relativity, and ADM Formalism" (2022). Student Research Submissions. 454.