Module Catalogues, Xi'an Jiaotong-Liverpool University
Module Code:
MTH304
Module Title:
Relativity
Module Level:
Level
3
Module Credits:
5.00
Academic Year:
2019/20
Semester:
SEM2
Originating Department:
Mathematical Sciences
Pre-requisites:
MTH209
Aims
To impart
(i) a firm grasp of the physical principles behind Special and General Relativity and their main consequences;
(ii) technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;
(iii) knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;
(iv) basic concepts of black holes and (if time) relativistic cosmology.
Learning outcomes
A. Understand why space-time forms a non-Euclidean four-dimensional manifold.
B. Perform calculations involving Lorentz transformations, energy-momentum conservation and the Christoffel symbols proficiently.
C. Understand the arguments leading to Einstein’s field equations, and how Newton’s law of gravity arises as a limiting case.
D. Explain the construction of the Schwarzschild solution and describe the trajectories of bodies within it.
Method of teaching and learning
This module will be delivered using formal lectures.
Syllabus
Newtonian mechanics and its limitations.
Principles of special relativity.
Lorentz transformation: derivation, properties.
Relativistic kinematics: length contraction, time dilation, velocity addition.
Minkowski space formulation.
Relativistic particle mechanics: energy-mass relation, four-Riemann space, Properties of tensors.
Parallel displacement, geodesics, covariant derivatives.
Curvature tensor and scalar, Ricci tensor.
Equivalence principle, gravitational time dilation, non-Euclidean spacetime.
Freely falling bodies, weak field limit.
Field equations, cosmological constant.
Schwarzschild solution and its geodesics.
Classical tests of General Relativity.
Black holes.
Time permitting: Basics of cosmology, Robertson-Walker metric, Friedman
Delivery Hours
Lectures
Seminars
Tutorials
Lab/Prcaticals
Fieldwork / Placement
Other(Private study)
Total
Hours/Semester
52
98
150
Assessment
Sequence
Method
% of Final Mark
1
Open-Book Quiz
15.00
2
Take-Home Open Book Exam
85.00
Module Catalogue generated from SITS
CUT-OFF: 6/5/2020 8:48:47 PM