Relativity Theory I
Special relativity and tensors
Galilean relativity and 3-vectors. Special relativity and 4-vectors. Relativistic particles. Electromagnetism. Constant relativistic acceleration.
Equivalence principle. Spacetime as a curved manifold. Tensors in curved spacetime. Rules for tensor index gymnastics.
The covariant derivative
How basis vectors change: the affine connection. Covariant derivative and parallel transport. Geodesic equations.
Curvature and Riemann tensor. Riemann normal coordinates and the Bianchi identity. Information in Riemann.
The physics of curvature
Geodesic deviation. Tidal forces. Taking the Newtonian limit.
The power of symmetry, and Einstein's equations
Lie derivatives. Killing tensors. Maximally symmetric spacetimes. Einstein's equations.
Black hole basics
Birkhoff's theorem and the Schwarzschild solution. TOV equation for a star. Geodesics of Schwarzschild.
More advanced aspects of black holes
Causal structure of Schwarzschild. Reissner-Nordstrom black holes. Kerr black holes. The Penrose process.
Classic experimental tests of GR
Gravitational redshift. Planetary perihelion precession. Bending of light. Radar echoes. Geodesic precession of gyros. Accretion disks.
Behaviour of light in gravitational fields. Deflection angles. Time delay. Magnification and multiple images.
Pre-class homework worth 20%, four problem sets worth 40% (10% each), midterm 15%, final exam 25%, real-time engagement in classes & tutorials 5%.
- Recommended preparation
['M.P. Hobson, G. Efstathiou, and A.N. Lasenby, General Relativity: An Introduction for Physicists (Cambridge, 2006).']
- course title
- year of study
- 4th year
- time and location
24L: LEC0101, LEC2001: MR11, all lectures in Room: MP134 12T: TUT0101: F1, Room: MP134
- Course URL