Course Code    : AMAT 42443

Title                   : Tensor Analysis and General Relativity

Pre-requisites   :  PMAT 21263

Learning Outcomes:

After the completion of this course unit, the student will be able to:
1. understand the concept of tensor variables and different from scalar or vector variables
2. understand the reason why the tensor analysis is used and explain usefulness of the tensor analysis
3. demonstrate the knowledge of concepts and theorems in tensor algebra
4. solve Einstein’s field equations in the simplest settings
5. understand the principles of general relativity and physics in curved spacetime
6. develop tools to enable the quantitative calculation of general relativistic effects
7. demonstrate knowledge and discuss the dynamic interactive physical processes in astrophysics using
general relativistic approach.

 Course Contents:

Introduction to tensors: Covariant and contravariant tensors, Metric tensor, Invariants.
Operations of tensors: Inner products, Differential-forms, Christoffel symbols and Covariant differentiation of
tensors, The geodesic equation, Riemann tensor, Ricci tensor, Einstein tensor, Bianchi identities,
General Relativity: Introduction to General Relativity, Einstein’s field equations, Schwarzchild interior and
exterior solutions, Black holes, Rotating systems, Tests in general relativity: Gravitational red shift, Bending of
light and gravitational lenses.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

1. Adler, R., Bazin, M. & Schiffer, M. (1975). Introduction to General Relativity, McGraw Hill, New York.
2. Misner, C.W., Thorne, K.S. & Wheeler, J.A. (2017). Gravitation, Princeton University Press.
3. Hawking, S.W. & Ellis, G.F.R. (1975). The Large-Scale Structure of Space-time, Cambridge University Press.
4. Hartle, J.B. (2013). Gravity: An Introduction to Einstein's General Relativity, Pearson.