General Covariance

Abstract

The general theory of relativity is introduced based on the principle of equivalence. Gravity is shown to arise dues to spacetime curvature. Specific examples of curved spacetimes are presented from the approximate but more intuitive to the complex: Uniform gravitational field (Galilean metric), the Newtonian weak field metric, Schwarzschild’s exterior and interior solutions, black holes, and cosmological spacetimes. A brief discussion on distances, areas and volumes in curved spaces is also given.