# The Einstein field equations, part I: the right-hand side

by Atle Hahn (GFMUL, Universidade de Lisboa, Portugal)

This lecture is an introduction to Einstein's "field equations" of General Relativity. The main emphasis is on the so-called "stress-energy tensor", which is often ignored by mathematicians but is crucial in most concrete applications, like, e.g., the Friedmann model of the big bang. After a brief overview over Special and General Relativity I will define and study the properties & applications of the classical stress tensor in non-relativistic fluid dynamics. Then I will show how the stress-energy tensor arises naturally from the stress tensor by making the transition from 3d Euclidean space to Minkowski space. The lecture concludes with a discussion of the properties and the explicit form of the stress-energy tensor for the relativistic perfect fluid and the pure electromagnetic field (this covers many of the most important applications in General Relativity). The lecture is directed to a broad audience. Hopefully, both mathematicians (at graduate level) and physicists (at advanced undergraduate level) will be able to benefit.