Date of Award

Spring 4-29-2022

Document Type

Honors Project

Degree Name

Bachelor of Science



Department Chair or Program Director

Esunge, Julius

First Advisor

Chiang, Yuan-Jen

Second Advisor

Esunge, Julius

Third Advisor

Sumner, Suzanne

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.