General Relativity

One of the most interesting applications of Riemannian geometry outside mathematics is General Relativity, in which our universe is modeled by a manifold and the gravitational field g is interpreted as a non-positive definite quadratic form. The purpose of this chapter is to make plausible the fundamentals of this theory, such as the field equation of gravity, by rigorously deriving them, following Hilbert, from a few simple assumptions.