- UCAS course code
- F305
- UCAS institution code
- M20
Master of Physics (MPhys)
MPhys Physics
Join a physics Department of international renown that offers great choice and flexibility, leading to master's qualification.
.jpg)
Duration: 4 years
Year of entry: 2025
UCAS course code: F305 / Institution code: M20
- Key features:
Scholarships available
Accredited course
- Typical A-level offer: A*A*A including specific subjects
- Typical contextual A-level offer: A*AA including specific subjects
- Refugee/care-experienced offer: AAA including specific subjects
- Typical International Baccalaureate offer: 38 points overall with 7,7,6 at HL, including specific requirements
Fees and funding
Fees
Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £36,500 per annum. For general information please see the undergraduate finance pages.
Policy on additional costs
All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).
Scholarships/sponsorships
The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.
For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .
Course unit details:
Gravitation (M)
| Unit code | PHYS40771 |
|---|---|
| Credit rating | 10 |
| Unit level | Level 4 |
| Teaching period(s) | Semester 1 |
| Available as a free choice unit? | No |
Overview
Gravitation (M)
Pre/co-requisites
| Unit title | Unit code | Requirement type | Description |
|---|---|---|---|
| Advanced Dynamics | PHYS10672 | Pre-Requisite | Optional |
| Lagrangian Dynamics | PHYS20401 | Pre-Requisite | Recommended |
| Cosmology | PHYS30392 | Pre-Requisite | Optional |
| Complex Variables and Vector Spaces | PHYS20672 | Pre-Requisite | Recommended |
| Electrodynamics (M) | PHYS30441 | Pre-Requisite | Recommended |
For recommneded theroty units following this module please see PHYS40722
Aims
Development of the ideas of General Relativity within the framework of differential geometry on a curved manifold.
Learning outcomes
On completion successful students will be able to:
- apply the basic concepts of differential geometry on a curved manifold, specifically the concepts of metric, connection and curvature.
- use the Einstein equations to describe the relation between mass-energy and curvature
- understand the relation of General Relativity to Newtonian theory and post-Newtonian corrections, including gravitational waves.
- describe spherical Black Holes.
- derive the basic properties of the FLRW Universe.
Syllabus
The weakest of all the fundamental forces, gravity has fascinated scientists throughout the ages. The great conceptual leap of Einstein in his 'General Theory of Relativity' was to realize that mass and energy curve the space in which they exist. In the first part of the course we will develop the necessary mathematics to study a curved manifold and relate the geometrical concept of curvature to the energy momentum tensor. In the second part of the course we solve the Einstein equations in a number of simple situations relevant to the solar system, black holes, and a homogeneous and isotropic universe.
Preliminaries (4 lectures)
Cartesian Tensors; Variational Calculus; Newtonian mechanics and gravity; Review of Special Relativity; Einstein's lift experiment; Einstein's vision of General Relativity, Rindler space.
Manifolds and differentiation (2lectures)
Manifolds, curves, surfaces; Tangent vectors; Coordinate transformations; Metric and line element; Vectors, co-vectors and tensors; Conformal metrics.
Connection and tensor calculus (4 lectures)
Covariant differentiation and Torsion; Affine Geodesics; Metric Geodesics and the Metric Connection; Locally Inertial Coordinates; Isometries and Killing's Equation; Computing Christoffel symbols and Geodesics.
Curvature (2 lectures)
Riemann Tens
Assessment methods
| Method | Weight |
|---|---|
| Written exam | 100% |
Feedback methods
Feedback will be available on students’ individual written solutions to selected examples, which will be marked when handed in, and model answers will be issued
Recommended reading
The following texts are useful for revising the material for the course
Cheng, T. P., Relativity, Gravitation and Cosmology: A Basic Introduction (second edition, Cambridge University Press, 2010)
D'Inverno, R. Introducing Einstein's Relativity, (Oxford University Press, 1992)
Hartle, J. B. An Introduction to Einstein's General Relativity, (Addison Wesley, 2004)
Hobson, M. P., Efstathiou, G. & Lasenby, A. N. General Relativity: An Introduction for Physicists (Cambridge University Press, 2006)
Lambourne, R. J. A., Relativity, Gravitation and Cosmology (Cambridge University Press, 2010)
More advanced texts
Misner, C.W. Thorne, K.S & Wheeler, J.A. Gravitation, (Freeman)
Wald, R.M. General Relativity (University of Chicago Press)
Study hours
| Scheduled activity hours | |
|---|---|
| Assessment written exam | 1.5 |
| Lectures | 24 |
| Work based learning | 6 |
| Independent study hours | |
|---|---|
| Independent study | 68.5 |
Teaching staff
| Staff member | Role |
|---|---|
| Michael Seymour | Unit coordinator |