In this article we will be presenting an overview of the mathematical formulation and foundations of General Relativity. Basic objects such as the metric tensor and the connection are introduced, and given a geometric interpretation. The structure and meaning of the Einstein Field Equations will be discussed in more detail, a recipe for solving them will be presented, and the calculation of geodesics will be explained.
Prerequisits : Special Relativity for Laypeople, Special Relativity : The Rest Of The Story Recommended : Manifolds and Curvature The purpose of this article is to introduce the basic concepts of what GR is about, without getting lost in mathematics, but also without succumbing to the “easy way out”, as given by seemingly simple yet highly misleading […]
We introduce the basic concepts of differential geometry on manifolds. We define manifold, and explain the reasoning behind connections. This leads us on to the covariant derivative, and eventually to the Riemann curvature tensor, as well as the Ricci tensor. The geometric meaning of these objects is explained.