Einstein Equations, Schwarzschild Solution, and Gravitational Waves

Abstract

In order to formulate the equations for the metric, the first step is to consider an alternative definition of the energy–momentum tensor of particles and fields. In Chap. 2, we already learned the canonical definition of the energy and momentum conservations in classical mechanics and the energy–momentum tensor of particles and fields in special relativity. It happens that in general relativity, things somehow turn out to be simpler—here, we gain an alternative and in fact more economic, dynamical definition of the energy–momentum tensor.