Introduction to General Relativity
LECTURER: N.T. Bishop
The module is intended to be accessible to any student who has majored in mathematics, applied mathematics, or physics. The essential mathematical tool on which the subject is built is vector calculus.
The mathematical tools of general relativity: vectors and tensors in general coordinates, tensor calculus, the covariant derivative, Riemann curvature tensor, Ricci tensor, Einstein tensor (10 lectures).
Special relativity: equivalence of inertial observers, constancy of the speed of light, Lorentz transformation, Minkowski spacetime (4 lectures).
Physical foundations of general relativity: equivalence principle, spacetime is not flat, Einstein’s equations (“geometry = matter”), linearized static approximation, geodesic motion (6 lectures).
Schwarzschild vacuum metric: solution of Einstein equations under spherical symmetry, Birkhoff’s theorem, classical tests (bending of light, perihelion precession, spectral red-shift) (6 lectures).
J. Foster & J.D. Nightingale “A short course in general relativity, 3rd Edition”, Springer 2006
One tutorial per week.
Two tests and one final examination.