Synopsis for C7.2b: General Relativity II

Recommended Prerequisites

B7.1a, C7.2a General Relativity I

Aims & Objectives

In this, the second course in General Relativity, we have two principal aims. We first aim to increase our mathematical understanding of the theory of relativity and our technical ability to solve problems in it. This leads to a greater understanding of the Schwarzschild solution and an introduction to its rotating counterpart, the Kerr solution. Then we apply the theory to a wider class of physical situations, notably to the problem of constructing a cosmological model to represent the universe itself in the large.

Synopsis

The Lie derivative and isometries. Linearised General Relativity and the metric of an isolated body. The Schwarzschild solution and its extensions; Eddington-Finkelstein coordinates and the Kruskal extension. Stationary, axisymmetric metrics and orthogonal transitivity; the Kerr solution and its properties; interpretation as rotating black hole. The Einstein field equations with matter; the energy-momentum tensor for a perfect fluid; equations of motion form the conservation law. Cosmological principles, homogeneity and isotropy; cosmological models; the Friedman–Robertson–Walker solutions; observational consequences.

Method of Examination

4 examination questions.

1. L. P. Hughston and K. P. Tod, An Introduction to General Relativity, LMS Student Text 5, CUP (1990), Chs.19, 20, 22-26.
2. R. M. Wald, General Relativity, Univ of Chicago Press (1984).