Applied Mathematics
MP403: Cosmology and General Relativity (5 ECTS)
In the study of cosmology where gravitation is the dominant force over the large scales considered, general relativity is the basic component. This course introduces general relativity. Topics covered include geometry, geodesics, black holes, different model universes and cosmogony.
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Find the Gaussian curvature of a 2-dimensional space;
- Use the Euler-Lagrange equations to find the geodesics of a space-time;
- Derive of the Schwarzschild solution of Einstein's field equations using physical arguments;
- Find the event horizon of a spherically symmetric black hole;
- Use the concepts of general relativity to derive the Robertson-Walker line element;
- Use dimensional analysis to derive the Friedmann equation;
- Classify the solutions of the Friedman equation and the model universes they describe.
Indicative Content
- Introduction: review of Newtonian mechanics and Special Relativity;
- Geometry: intrinsic and extrinsic definitions of curvature, the metric tensor, Gauss curvature formula;
- Geodesics: the variational method, using the Euler-Lagrange equations to calculate geodesics;
- General Relativity: the postulates of General Relativity; Einstein's field equations, derivation of the Schwarzschild solution of Einstein's field equations using physical arguments;
- Cosmology: the cosmological principle, derivation of the Robertson-Walker line element, object and event horizons, the Friedman equation, cosmogony.
Module Resources
- Principles of Cosmology and Gravitation, by M. Berry
- Introducing Einstein's Relativity, by R. d'Inverno
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