PHYM006 - Module Description

MODULE TITLE	Relativity and Cosmology					CREDIT VALUE	15
MODULE CODE	PHYM006		MODULE CONVENER			Prof. T.J. Harries

DURATION	TERM	1	2	3	Number Students Taking Module (anticipated)		32
	WEEKS		T2:01-11

DESCRIPTION – summary of the module content (100 words)

This module is an introduction a cornerstone of 20th century physics, the general theory of relativity, Einstein's geometric theory of gravity. The module begins with a recap of special relativity. Subsequently, the mathematical tools (tensor analysis and differential geometry) that underpin general relativity are presented, and students will require a good level level of mathematical fluency and intuition in order to engage with material. Topics include Einstein's field equation, Schwarzschild's solution and black holes, gravitational waves, and the Robertson-Walker metric and cosmology.

MODULE AIMS – intentions of the module

The module aims to develop an understanding of Einstein's theory of general relativity (GR). The module starts with a recap of special relativity and then introduces the principles of equivalence, covariance and consistency that lead Einstein to the general theory. The mathematics of tensors and differential geometry are presented in the context of Einstein's field equation. This is followed by a detailed derivation of Schwarzchild's solution and its implication for time and space around a black hole. The module concludes by examining the use of GR in cosmology.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

give coherent explanations of the principles associated with: special relativity, general relativity, and cosmology;
interpret observational data in terms of the standard model of the evolution of the Universe;
describe experiments and observational evidence to test the general theory of relativity, explain how these support the general theory and can be used to criticise and rule-out alternative possibilities;
apply tensors to the description of curved spaces;
solve problems by applying the principles of relativity;
deduce the Friedmann equations describing the evolution of the Universe.
explain what is meant by: intrinsic and extrinsic curvatures, the curvature of space, local inertial reference frame, and Riemannian coordinates/geometry;
describe world lines of particles and photons in a curved space-time;
describe the cosmological principle and the Robertson-Walker metric;

Discipline Specific Skills and Knowledge:

explain to non-specialists the basis of one of the corner-stones of 20th century physics;

Personal and Key Transferable / Employment Skills and Knowledge:

locate, retrieve and evaluate relevant information from the WWW;
meet deadlines for completion of work to be discussed in class by developing appropriate time-management strategies.

SYLLABUS PLAN – summary of the structure and academic content of the module

Introduction
Recap of key aspects of special relativity
1. Galilean and Lorentz transformations
2. Length contraction and time dilation
3. Doppler effect
4. Relativistic mechanics
Tensor analysis
1. Covariant and contravariant tensors
2. Reciprocal basis vectors
3. Tensor algebra
4. The metric tensor
5. Christoffel symbols and covariant differentiation
6. The geodesic equation
Curved spaces
1. Intrinsic and extrinsic curvature
2. Parallel transport
3. Riemannian curvature
4. Ricci tensor and scalar
Einstein's field equation
1. The stress-energy tensor
2. Einstein's field equation
3. The weak field limit
4. Schwarzschild's solution
5. Black holes and singularities
Black holes
1. Geodesic equations, orbital shape equation
2. Falling into a black hole
3. Eddington-Finkelstein coordinates
4. Rotating black holes and the Kerr metric
5. Frame dragging and ergosphere
Gravitational waves
1. Linearised gravity
2. Wave equation
3. Weak gravitational waves
4. The motion of a test particle
5. Detecting gravitational waves
Cosmology
1. The cosmological principle
2. Robertson-Walker metric
3. Red-shift distance relation
4. The Friedmann equations
5. Inflation
Additional Topics
1. Eotvos experiments
2. Observational tests of GR
3. A recap of special relativity
4. An introduction to tensor mathematics
5. Derivation of the Friedmann equations from the Robertson-Walker metric

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching activities

22 hours

Guided independent study

128 hours

Placement/study abroad

0 hours

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS