General Relativity — Foundations

From the equivalence principle to black holes, gravitational waves and cosmology.

Syllabus

  1. Foundations — From Equivalence to Geometry

    1. The Equivalence Principle
    2. Spacetime & the Metric
    3. Geodesics — The Straightest Path
    4. Proper Time & the Gravitational Twin
    5. Gravitational Redshift

  2. The Schwarzschild Solution and the Classical Tests

    1. The Schwarzschild Metric
    2. Orbits I — The Effective Potential
    3. Orbits II — Mercury's Precession
    4. Bending of Light
    5. Lensing & the Shapiro Delay

  3. Black Holes

    1. Black Holes — The Horizon
    2. Falling In — Spaghettification
    3. Spin & Shadow — Kerr and the EHT Image

  4. Curvature, the Field Equations and the Universe

    1. Curvature, Concretely: Geodesic Deviation
    2. The Riemann Curvature Tensor
    3. The Einstein Field Equation
    4. Gravitational Waves
    5. Cosmology: General Relativity and the Universe