Official description

Special relativity and tensors

Galilean relativity and 3-vectors. Special relativity and 4-vectors. Relativistic particles. Electromagnetism. Constant relativistic acceleration.

Spacetime

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.

Spacetime curvature

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.

Gravitational lensing

Behaviour of light in gravitational fields. Deflection angles. Time delay. Magnification and multiple images.

ASSESSMENT

Pre-class homework worth 20%, four problem sets worth 40% (10% each), midterm 15%, final exam 25%, real-time engagement in classes & tutorials 5%.