Registry
Module Specifications
Archived Version 2022  2023
 
Description This module provides students with the mathematical tools required to study General Relativity (GR), and introduces them to the area. The module includes the study of the conceptual foundations of GR and Einstein's equation, the study of the Schwarzschild solution, and the analysis of the classical tests of GR.  
Learning Outcomes 1. Complete a range of calculations relevant to the mathematics of curved spacetime (tensor algebra, metrics, connections, curvature, geodesics, isometries). 2. Use computer algebra to carry out a range of calculations relevant to the mathematics of curved spacetime. 3. Solve a range of problems relating to the mathematics of curved spacetime. 4. Apply their knowledge of differential geometry to describe and analyse different phenomena of gravitational fields. 5. Apply their knowledge of differential geometry to solve a range of problems relating to gravitational fields. 6. Analyse the conceptual foundations of General Relativity and discuss how these limit possible theories of gravitation. 7. Compare and contrast General Relativity with other theories of gravitation, both conceptually and in terms of observational evidence.  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and
Learning Activities Differential Geometry Tensor algebra. Manifolds, curves and tangent vectors. Connections and covariant derivatives. Metric tensors and the metric connection. Geodesics and geodesic deviation. Curvature. The Riemann, Ricci and Einstein tensors. Lie derivatives, isometries and Killing vectors. Conceptual foundations of GR The weak and strong equivalence principles. The energymomentum tensor. Einstein's field equation. The cosmological constant. Alternative theories of gravity. The Schwarzschild Solution. Birkhoff's theorem and derivation of the Schwarzschild solution. Geodesics in the Schwarzschild exterior. Null geodesics and the KruskalSzekeres extension. Singularities in Schwarzschild spacetime. Classical test of GR Gravitaional redshift. Bending of starlight. Precession of the perihelion of Mercury. Observational data and alternative theories.  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes  
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