Module code: PHYM053

Module Overview

This module will introduce the students to the principles and formalism of General Relativity and its applications to Black Holes and astrophysical phenomena.

Module provider

Mathematics & Physics

Module Leader

GUALANDRIS Alessia (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 85

Lecture Hours: 22

Laboratory Hours: 11

Guided Learning: 10

Captured Content: 22

Module Availability

Semester 2

Prerequisites / Co-requisites

Programming skills in either Python, C, C++ or Fortran are required.

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

Assessment pattern

Assessment type Unit of assessment Weighting
Examination End of semester examination - 2 hour 70

Alternative Assessment


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 general relativity.
Thus, the summative assessment for this module consists of:

• A coursework based on the computational project developed during the module.
• A 2 hour final examination with two sections: Section A contains compulsory questions worth 20 marks & Section B contains three questions of 20 marks each of which the students attempt two.

Formative assessment and feedback

During lectures students will have group problems to apply theory covered with direct
interaction with the lecturer and feedback on their understanding.
The students will be assisted in the development of the computer code and will receive verbal feedback during the lab sessions.

Module aims

  • This module aims to:
    • Give the students a clear understanding of the limits of Newtonian mechanics and
    Special Relativity
    • Introduce the principles and formalism of General Relativity
    • Show how to apply the Post Newtonian approximation to astrophysical systems

Learning outcomes

Attributes Developed
001 Understanding of the concept of tensors, manipulate simple tensorial equations and understand the elements of differential geometry in relation to describing curved space-times KCPT
002 Understanding of Einstein field equations which describe the gravitational field arising from any distribution of matter KC
003 Ability to solve problems involving the motion of observers around a central mass point. KPT
004 Understanding of the key tests of general relativity and show how the predictions of this theory deviate from Newtonian theory KC
005 Ability to describe the behaviour of observers in the vicinity of a black hole which has no charge or rotation KCT
006 Ability to 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 KCT
007 Understanding of the Post Newtonian approximation and implement it in a numerical N-body integrator KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to enable students to understand the fundamental concepts involved in General
The learning and teaching methods include:
• Lectures

• Computer Lab

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: PHYM053

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability, and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities. The module features a computing project aimed at writing a 2-body orbit integrator that accounts for relativistic effects. The students can program in either Python, C, C++ or Fortran and develop their codes from start to end, gaining confidence in coding and checking results against theoretical predictions.

Employability.  The students work on a challenging computational project, gaining experience in all stages of code development, from algorithm implementation to debugging and visualisation. The students then need to describe the results of the project in a report, which is written in the style of a scientific article. The students also learn advanced mathematics concepts including differential geometry and tensor calculus.

Resourcefulness and Resilience. Problem solving is a key component of this module with students working on both theoretical calculations in relativity and numerical simulations.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Nuclear Astrophysics MPhys 2 Optional 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 MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module
Physics with Quantum Computing MPhys 2 Optional 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 MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MMath 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 2025/6 academic year.