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

Independent Study Hours: 117

Lecture Hours: 22

Laboratory Hours: 11

Assessment pattern

Assessment type Unit of assessment Weighting

Alternative Assessment


Prerequisites / Co-requisites

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 Newtonian Mechanics 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

Indicative content includes:

Introduction (2 hours)

Inadequacy of Newtonian Gravity

Inadequacy of Special Relativity

Mach's Principle

Einstein's Principle of Equivalence

Mathematics of General Relativity (6 hours)

Tensors and Special Relativity

Covariant derivatives

Geodesics and Parallel Transport

Principles of General Relativity (4 hours)

Einstein's Field Equations

The Schwarzchild Solution

Classical tests of General Relativity

Black Holes

Cosmology (10 hours)

Relativistic Cosmology

Dark Matter and Dark Energy

Observational Cosmology and the Cosmic parameters

Matter-radiation coupling

Inflationary models

The Early Universe

Methods of Teaching / Learning

The learning and teaching strategy is designed to increase students’ critical understanding of physics and astrophysics, and through this module to provide students with the opportunity to explore both the theoretical and experimental concepts of General Relativity.

The learning and teaching methods include:

lectures + tutorials (2hrs per week x 11 weeks)

computational assignment (11hrs)

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate core competencies in astrophysics topics, through the use of examination and coursework. Additionally, the coursework assignment will develop the students' programming and problem solving skills.

Thus, the summative assessment for this module consists of:

a written examination of 1.5hr duration, with 2 questions from 3 to be attempted

a computing project, in which students will model the motion of stars orbiting in Schwarzschild and Kerr metrics –that describe non-rotating and rotating black holes. They will consider how "post-Newtonian" terms due to General Relativity (GR) perturb the otherwise Keplerian orbits and show how this affects the orbit of Mercury in the Milky Way, and the orbits of stars around the supermassive black hole at the centre of our Galaxy. They will compare and contrast orbital precession due to GR with orbital precession due to an extended distribution of mass.

Reading list

Reading list for GENERAL RELATIVITY :

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module
Physics with Quantum Technologies MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module
Physics with Nuclear Astrophysics MPhys 2 Compulsory A weighted aggregate mark of 50% is required to pass the module
Physics with Astronomy MPhys 2 Compulsory A weighted aggregate mark of 50% is required to pass the module
Physics MSc 2 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MMath/MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module

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.