General Relativity

Abstract

Abstract. General relativity, or the general theory of relativity, is the geometric theory of gravitation. Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

Introduction

We all know that the most famous equation in physics is \(E=mc^2\)

This is Albert!

Field Equations

Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell’s equations, the EFE are used to determine the spacetime geometry resulting from the presence of mass-energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation. However It is also fairly easy to show that \[G_{\mu\nu}+ \Lambda g_{\mu\nu}=\frac{8 \pi G}{c^4}T_{\mu\nu}\] These field equatio