Study information

Relativity and Cosmology - 2024 entry

MODULE TITLERelativity and Cosmology CREDIT VALUE15
MODULE CODEPHYM006 MODULE CONVENERProf Tim Harries (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 32
DESCRIPTION - summary of the module content

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 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.

Pre-requisite modules: PHY1021, PHY1022, PHY2025 or equivalent modules.

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)
A student who has passed this module should be able to:
 
Module Specific Skills and Knowledge:
1. give coherent explanations of the principles associated with: special relativity, general relativity, and cosmology;
2. interpret observational data in terms of the standard model of the evolution of the Universe;
3. 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;
4. apply tensors to the description of curved spaces;
5. solve problems by applying the principles of relativity;
6. deduce the Friedmann equations describing the evolution of the Universe.
7. explain what is meant by: intrinsic and extrinsic curvatures, the curvature of space, local inertial reference frame, and Riemannian coordinates/geometry;
8. describe world lines of particles and photons in a curved space-time;
9. describe the cosmological principle and the Robertson-Walker metric;
 
Discipline Specific Skills and Knowledge:
10. explain to non-specialists the basis of one of the corner-stones of 20th century physics;
 
Personal and Key Transferable / Employment Skills and Knowledge:
11. locate, retrieve and evaluate relevant information from the WWW;
12. 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
I. Introduction
II. Recap of key aspects of special relativity
  1. Galilean and Lorentz transformations
  2. Length contraction and time dilation
  3. Doppler effect
  4. Relativistic mechanics
III. 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
IV. Curved spaces
  1. Intrinsic and extrinsic curvature
  2. Parallel transport
  3. Riemannian curvature
  4. Ricci tensor and scalar
V. 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
VI. 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
VII. Gravitational waves
  1. Linearised gravity
  2. Wave equation
  3. Weak gravitational waves
  4. The motion of a test particle
  5. Detecting gravitational waves
VIII. Cosmology
  1. The cosmological principle
  2. Robertson-Walker metric
  3. Red-shift distance relation
  4. The Friedmann equations
  5. Inflation
IX. 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 Guided Independent Study 128 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 20 20×1-hour lectures
Scheduled learning and teaching activities 2 2×1-hour problems/revision classes
Guided independent study 30 5×6-hour self-study packages
Guided independent study 16 4×4-hour problem sets
Guided independent study 82 Reading, private study and revision

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Guided self-study 5×6-hour packages (fortnightly) 1-12 Discussion in class
4 × Problems sets 4 hours per set (fortnightly) 1-12
Solutions discussed in problems classes

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Final Examination 100 2 hours 30 minutes 1-10 Written, collective feedback via ELE and solutions.

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Final Examination Written examination (100%) 1-12 Referral/deferral period

 

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.
 
Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Core text:

  • Lambourne R. (2010), Relativity, Gravitation and Cosmology, Cambridge, ISBN 9-7805-2113-1384 (UL: 530.11 LAM/X)

Supplementary texts:

  • Coles P. and Lucchin F. (2002), Cosmology - the Origin and Evolution of Cosmic Structure (2nd edition), Wiley, ISBN 978-0-471-48909-2 (UL: 523.1 COL)
  • Hartle J.B. (2003), Gravity: An Introduction to Einstein's General Relativity, Addison-Wesley, ISBN 978-0-805-38662-2 (UL: 530.11 HAR)
  • Kenyon I. (1990), General Relativity, Oxford University Press (UL: 530.11 KEN)

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES PHY1021, PHY1022, PHY2025
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Wednesday 13th March 2024 LAST REVISION DATE Tuesday 21st May 2024
KEY WORDS SEARCH Physics; Theory; Spaces; Curvature; Time; Curves; General theory; Shifts; Cosmological; Equation; Inertial frame.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.