Course Archives    Theoretical Statistics and Mathematics Unit

Course: General Relativity Level: Undergraduate Time: Currently not offered

Syllabus Past Exams Syllabus Review of Special Relativity, Spacetime diagrams and four-vectors Gravity as geometry: the equivalence principle, clocks in a gravitational field The Description of Curved Spacetime: metric, Penrose diagrams, local inertial frames, light cones and world lines, embedding diagrams, vectors in curved space-time The Geodesic Equation: Solving the geodesic equation- symmetries and conservation laws, Killing vectors, null geodesics, local inertial frames and freely falling frames Schwarzschild geometry, the gravitational redshift, particle and light ray orbits, Solar system tests of General Relativity Schwarzschild Black hole, Kruskal-Skekeres coordinates Vectors, Dual Vectors, Covariant Derivatives Equation of Geodesic Deviation, Riemann Curvature, Einstein Equation in vacuum. The Source of Curvature: Densities, Conservation Laws, Einstein Equation with matter-energy as a source Cosmological Solutions of Einstein’s Equations. Robertson-Walker metric. ( If time permits) Reference Texts: 1. Gravity: An Introduction to Einstein’s General Relativity - James Hartle. 2. A First Course in General Relativity- B. Schutz 3. Spacetime and Geometry: An Introduction to General Relativity- Sean M. Caroll Top of the page Past Exams

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