#### Date of Award

Spring 5-7-2016

#### Document Type

Honors Project

#### Degree Name

Bachelor of Science

#### Department

Mathematics

#### First Advisor

Chiang, Yuan-Jen

#### Second Advisor

Helmstutler, Randall

#### Major or Concentration

Mathematics

#### Abstract

Classically, the physics of the universe is described by Newton's Laws of Motion and Newton's Law of Universal Gravitation. In most cases, the results predicted by Newton's theories accurately agree with experimental observations. However, under certain limitations, classical theories may yield slight deviation from observations, such as when the speed of an object approaches the speed of light. At the extreme, classical theory completely fails to explain the motion of photons, which are massless particles of light. In 1915, Albert Einstein published the General Theory of Relativity. Einstein's theory provides a new perspective to a better understanding of the physics describing this universe. In this paper, we attempt to introduce some of the prerequisite material in differential geometry and investigate the general theory of relativity, along with some of its solutions from a mathematical point of view. We study homogeneous and isotropic cosmology, and the Schwarzschild solution. Finally, we will discuss some of their applications and significance.

#### Recommended Citation

Zhang, Pengcheng, "Homogeneous and Isotropic Cosmology, the Schwarzschild Solution, and Applications" (2016). *Student Research Submissions*. 62.

https://scholar.umw.edu/student_research/62