Einstein Field Equations and the Solutions for Uncharged Black Holes

Abstract

The General Theory of Relativity, formulated by the brilliant mind of Albert Einstein, stands as one of the most fundamental and revolutionary pillars of modern physics. This elegant theory of gravity not only offers a comprehensive explanation of the workings of the universe on a large scale, but it has also paved the way for groundbreaking advancements in the field of mathematics. This thesis begins by providing a concise overview of the key mathematical principles that are crucial to understanding Einstein’s theory. These principles form the basis for deriving the field equations that Einstein introduced. From there, these equations are expertly applied to explore solutions related to uncharged black holes, such as Schwarzschild and Kerr solutions, along with their corresponding geodesic equations.