[Home] Introduction to General Relativity. Pensumlist

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1. Curvilinear coordinates.
   • (Jimi) Einstein's equivalence principle (DI 9.4)^*.
   • Curvilinear coordinates. Covariant differentiation and Christoffel symbols. Geodesic as a "no-acceleration" trajectory. (DI 6.3,6.4)
   • Metric tensor. Geodesic from the variational principle. Connection between Christoffel symbols and the metric tensor. (DI 6.8,6.9,6.10,7.6)
   • Motion of a particle in a gravitational field. Maxwell equations in the presence of a gravitaional field. Motion of a particle in the presence of both gravitational and electromagnetic field.
2. Gravitational field equations
   • Riemann curvature tensor R^a_bcd. Properties of the curvature tensor. (DI 6.5)
   • Invariant volume element √(-g)dΩ. (DI 7.3)
   • Action for the gravitation field S = -¹/_2κ ∫ R√(-g)dΩ. (DI 11.3,11.4,11.5)
   • Energy-momentum tensor T_ab for the matter. (DI 11.8)
   • Gravitational field equations R_ab-½g_abR=κT_ab. (DI 11.8)
3. Solutions of the field equations
   • (Christian) Newton's law as the slow weak field limit of the Einstein's equations (DI 12.9,12.10).
   • Weak gravitational waves (DI 20.1,20.2).
   • (Karl) Centrally symmetric field. Schwarzschild metric. (DI 14.4-14.7)
   • Gravitational collapse (DI 16.4,16.5). Lemaitre metric.
   • (Morten) Mercury perihelon advance. Bending of light. Gravitational red shift (DI 15.3-15.5).
4. Relativistic cosmology.
   • Uniform and isotropic universe and its geometry (DI 22.6-22.8).
   • Friedmann's equation (DI 22.9).
   • Red shift and the Hubble constant (DI 22.12).

^* (DI x.y) means Ray D'Inverno, paragraph x.y

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Copyleft © 2003 D.V.Fedorov (fedorov@ifa.au.dk)