PHY483/1483F

Topics

This course concentrates on the basis for Einstein's theory of general relativity (GR), through an introduction to differential geometry, tensor analysis, and related topics, followed by the application of these ideas to gravitational physics, to lead to general relativity. GR is then studied from a number of points of view, including the simple black hole solutions of Schwarzschild, Kerr, and others. Attention will be focused on the physical basis and the mathematical properties of these solutions. As time permits, linkages to modern theories of gravity subsuming GR, such as string theory, will be made.

Syllabus

Topics covered are likely to include (not necessarily in this order):-

Reminder on special relativity; Lorentz transformations, vectors, tensors
Contant acceleration, equivalence principle
Spacetime as a manifold, coordinate transformations
Christoffel symbols
Geodesics
Vectors and tensors, bases
Special coordinate systems
Levi-Civita pseudotensor, Christoffel connection, frames
Covariant differentiation, Lie derivative
Riemann curvature
Energy-momentum tensor
Einstein field equations
Alternative theories of gravity
Solutions, symmetries
Black holes: Schwarschild, Reissner-Nordstrom, Kerr, Hawking radiation