General Relativity

for Differential Geometers

with emphasis on world lines rather than space slices

Philadelphia, Spring 2007

Hermann Karcher, Bonn


p. 2 Preface,

p. 3-11 Einstein's Clocks, a public lecture

p. 12-18 The simplest Pseudo-Riemannian examples

p. 19-25 Special Relativity I, basic definitions to Compton scattering

p. 26-33 Covariant differentiation, curvature properties, Jacobi fields

p. 34-42 Special Relativity II, Maxwell's equation and consequences

p. 43-52 Light Cone Geometry, 3-dim intuition versus 4-dim description

p. 53-62 Schwarzschild I, derivation and comparison with Newton

p. 63-86 II, Falling particles, bending of light, Shapiro delay, Perihelion advance, spinning planets, Kruskal extension, Kerr

p. 87-94 Stress Energy Tensor, simplest examples, geometric consequences

p. 95-109 Cosmological Models, derivation and model predictions