Course OutlineThis course is divided into seven major parts (although they are presented in more than seven chapters and there is significant interplay between the two). Principles of General Relativity – The nature of General Relativity is such that we can only really state the principles of General Relativity clearly at the end of the course. Still, they need to given an overview at the beginning, but we will come back to them regularly as our ability to understand them grows.
Differential Geometry – This is the mathematics that allows us to understand and make calculations with space-time curvature
Einstein’s Field Equations – In a sense, these equations are obvious once you understand space-time curvature, the various symmetries that need to be applied and the principles of general relativity.
The Schwarzschild solution - The solution to the field equations for a spherically symmetrical mass distribution – like the space-time around our sun.
The Newtonian Limit - Any new theory has to reproduce the successes of the theory (or theories) that it replaces, while going at least one step further. We will show that, in the appropriate limit, Einstein’s theories approximate Newton’s Gravitational Theory.
Experimental Tests of General Relativity - Anomalous precession of the perihelion of Mercury; Gravitational bending of light (the 1919 eclipse experiments of Eddington).
Black holes, Causal Structure of space-time, Penrose Diagrams – “modern General Relativity.”