General Relativity

PS1. Differential Geometry Manifolds, tensors, Lie and exterior derivatives, Maurer–Cartan, Poincaré lemma. HTML PDF Tong GR PS1
PS2. Connections & Curvature Christoffel transformation, torsion, Bianchi, parallel transport, Riemann / Ricci / Weyl, geodesics, Reissner–Nordström. HTML PDF Tong GR PS2
PS3. Geodesics, Killing Vectors & Energy Conditions Timelike geodesics, Brans–Dicke scalar-tensor gravity, 11-d supergravity, Killing vectors, conformal compactification, energy conditions. HTML PDF Tong GR PS3
PS4. Linearised Gravity & Gravitational Waves Linearised gravity from a point mass, cosmic strings, Lense–Thirring, Fierz–Pauli, transverse-traceless gauge, binary gravitational-wave emission. HTML PDF Tong GR PS4

3. Chapter 3: Curvature Torsion, two-dimensional geometry, Riemann symmetries, curvature, affine parameters, and geodesics. Selected worked problems. Includes links to related Tong GR solutions. HTML PDF Wald GR Ch. 3
4. Chapter 4: Einstein's Equation Maxwell theory, frame dragging, linearised gravity, and gravitational radiation. Selected worked problems. Includes links to related Tong GR solutions. HTML PDF Wald GR Ch. 4
5. Chapter 5: Homogeneous, Isotropic Cosmology Robertson-Walker coordinates, Friedmann equations, de Sitter spacetime, redshift, and null rays. Selected worked problems. HTML PDF Wald GR Ch. 5
6. Chapter 6: The Schwarzschild Solution Isotropic coordinates, Reissner-Nordström, stationary observers, a draft time-delay calculation, and horizon crossing. Selected worked problems. HTML PDF Wald GR Ch. 6