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## AMAT 42853: Tensor Analysis and General Relativity

**Course Code :** AMAT 42853

**Title :** Tensor Analysis and General Relativity

**Pre-requisites :** PMAT 21553

**Learning Outcomes: **

At the end of the course the student should be able to demonstrate knowledge of concepts and theorems in tensor algebra, tensor analysis and the formalism of general relativity, and to solve Einstein’s field equations in simple cases, and to apply the solutions in Astrophysics.

** ****Course Contents:**

Covariant and contravariant vectors, Metric tensor, Invariants, Inner products, Differential-forms, Tensor analysis, Covariant differentiation of tensors, Einstein’s field equations, Schwarzchild interior and exterior solutions, Rotating systems, Dragging of inertial frames, Gravitation 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:**

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