Module code: PHYM053

Module provider


Module Leader


Number of Credits


ECT Credits



FHEQ Level 7

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 2

Overall student workload

Lecture Hours: 22

Laboratory Hours: 11

Assessment pattern

Assessment type Unit of assessment Weighting

Alternative Assessment


Prerequisites / Co-requisites

The module will assume prior knowledge equivalent to the following modules.  If you have not taken these modules you should consult the module descriptors. PHY3038 Special Relativity; PHY2071 Introduction to Astronomy. Basic programming skills in either Fortran, C, C++ or Python are also required.

Module overview


This module will present the principles and basic formalism of General Relativity and provide the student with a deeper understanding of its applications to Black Holes, Cosmology and astrophysical phenomena.


Module aims

To give the student a clear understanding of the limits of NewtonianMechanics and Special Relativity. To provide a thorough description of the principles and formalism of General Relativity.

Learning outcomes

Attributes Developed
Judge the short-comings in the Newtonian theory of gravity, the problem of defining inertial frames, and the reasons why Special Relativity fails to resolve these issues KC
Understand the concept of tensors, manipulate simple tensorial equations and understand the elements of differential geometry in relation to describing curved space-times KC
Be familiar with the Einstein field equations which describe the gravitational field arising from any distribution of matter and will have a deeper understanding of the problems involving the motionof observers around a central mass point K
Understand the key tests of general relativity and show how the predictions of this theory deviate from Newtonian theory KC
Describe the behaviour of observers in the vicinity of a black hole which has nocharge or rotation KC
Understand the concordance Cosmological model and be able to assess the evidence that there is a need for dark matter and dark energy KC
Understand the interaction between the radiation and baryonic content of the Universe and the evolution of the early Universe K
Understand the basis of inflationary models and the problems in the standard model that these address K

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

General relativity lectures:

Introduction (inadequacy of Newtonian description, Special Relativity and Minkowski metric, Einstein’s principles of equivalence)

Mathematics of General Relativity (Forms, vectors and tensors, covariant derivatives and connections, parallel transport and geodesics, curvature)

Principles of General Relativity (Einstein’s field equations, the Schwarzschild solution, testing of General Relativity, black holes)

Gravitational radiation


General relativity computer lab:

The two-body problem in classical mechanics

Implementation of an N-body integrator to study the two-body problem

The Post-Newtonian approximation

Implementation of Post Newtonian corrections in the N-body integrator

Application of the N-body integrator to the study of 3 astrophysical problems:

Mercury’s precession of the perihelion, the orbits of the S-stars in the centre of the Milky Way, energy losses in black hole binaries due to emission of gravitational radiation


Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Enable students to understand the fundamental concepts involved in General Relativity.


The learning and teaching methods include:

Lectures: 2 hours lecture per week x 11 weeks

Computer Lab: 1 hour per week x 11 weeks


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate understanding of the formalism of general relativity, aspects of differential geometry relevant to gravitating systems and applications underpinning experimental tests of GR.


Thus, the summative assessment for this module consists of:

One final exam of 1.5 hours with 2 questions to be chosen out of 3.

One report to be submitted by the end of the course, including a listing of the computer code and a critical discussion of the results obtained for the 3 astrophysical problems.


Formative assessment and feedback

The students will be assisted in the development of the computer code and will receive verbal feedback during the lab sessions.

During lectures students will have group problems to apply theory covered with direct interaction with the lecturer and feedback on their understanding.


Reading list

Reading list for GENERAL RELATIVITY :

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.