General relativity
Graduate · Physics
Syllabus focus
Topics typically covered
Theoretical / proof-based
Geometric foundations
- Manifolds, tangent spaces, and tensors
- Affine connection and parallel transport
- Curvature: Riemann, Ricci, and Einstein tensors
- Geodesics and variational formulation
- Stress–energy conservation ∇_μ T^μν = 0
Einstein's equations
- Einstein field equations and Newtonian limit
- Schwarzschild solution and black holes
- Kerr metric and rotating black holes (intro)
- Linearized gravity and gravitational waves
- ADM formalism and 3+1 decomposition (overview)
Cosmology and tests
- FLRW metrics and Friedmann equations
- Gravitational lensing: weak and strong
- Perihelion precession and light deflection
- Gravitational time delay and Shapiro effect
- Initial value problem and gauge choices
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Geometric foundations
Manifolds, tangent spaces, and tensors
Coming soon - Einstein's equations
Einstein field equations and Newtonian limit
Coming soon - Cosmology and tests
FLRW metrics and Friedmann equations
Coming soon
Notes
Topics reflect common graduate physics core and elective syllabi at US universities. Sequencing and emphasis vary between one- and two-semester treatments.