Theoretical / proof-based
General relativity · Graduate · Physics
Topics
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
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.