Schwarzschild Spacetime and Friedmann-Lemaitre-Robertson-Walker Cosmology

The advent of General Relativity via Einstein\u27s field equations revolutionized our understanding of gravity in our solar system and universe. The idea of General Relativity posits that gravity is entirely due to the geometry of the universe -- that is, the mass distribution throughout the universe results in the curving of spacetime, which gives us the physics we see on a large scale. In the framework of General Relativity, we find that the universe behaves differently than was predicted in the model of gravitation developed by Newton. We will derive the general relativistic model for a simple system near a large mass, typically a star, which is spherical, static, and vacuum -- the result originally derived by Schwarzschild. The Schwarzschild model will be shown to explain the failure of Newtonian dynamics to predict the perihelion advance of the orbit of Mercury. Additionally, a model of the universe as a homogeneous, isotropic, perfect fluid made of particles that are galaxies (or galactic clusters or superclusters) will be developed under the conditions of the Einstein equation. This model, called the Friedmann-Lemaitre-Robertson-Walker (FLRW) model, will yield an upper bound for the age of the universe