# 2020/21 Taught Postgraduate Module Catalogue

## PHYS5390M General Relativity

### 15 creditsClass Size: 60

Module manager: Dr Stuart Lumsden
Email: S.L.Lumsden@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

### Pre-requisite qualifications

Level 2 Physics or equivalent – prior understanding of tensors is helpful but not essential; understanding of the basic principles of special relativity and differential calculus is essential. Prior study of differential geometry is not required.

Module replaces

PHYS5160M

This module is not approved as an Elective

### Module summary

This module introduces students to General Relativity. You will learn how to utilise techniques appropriate to differential geometry for familiar problems from Special Relativity before moving onto the study of how these methods can be used to derive the optimal means of studying particle dynamics in a curved space-time, and how physical laws can be translated into the same framework. The course will conclude with a study of applications of General Relativity including Cosmology and Black Holes.

### Objectives

You should be able to understand the underlying mathematical principles and techniques appropriate to General Relativity, as well as be able to apply them to simple physical cases by the end of this module.

Learning outcomes
- solve problems in special relativity using the formalism of tensor analysis;
- derive, and explain the basis for, the physical and mathematical principles of general relativity; derive equations governing spacetime geometry and the motion of particles in curved spacetimes;
- solve simple problems related to differential geometry and tensor calculus;
- describe the geometrical structures of Schwarzschild and Robertson-Walker spacetimes and their physical interpretations; derive and interpret the motions of light and massive particles in these cases.

Skills outcomes
- Ability to apply advanced mathematical methods and modelling techniques to physical problems.
- Ability to grasp a complex body of ideas.

### Syllabus

Review of special relativity, Lorentz transformations and particle dynamics. Introduction of metrics and tensors, and the role of invariance.

Geometry of space and time – the road to general relativity and the field equations. Differential geometry and tensor calculus: parallel transport, covariant derivative, curvature, geodesics. Metric: definition of length and angle, role in tensor calculus, metric connection.

Applications of the techniques of general relativity to spherical bodies, including black holes. Schwarzschild, and other, solutions. Meaning of distances and times in curved space and the role of the observer. Applications to Cosmology: Friedmann-Robertson-Walker models and the standard hot big bang.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Workshop 5 1.00 5.00 Office Hour Discussions 11 1.00 0.00 Lecture 22 1.00 28.00 Private study hours 117.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 150.00

### Private study

Working through unmarked problem sheets, reviewing and assessing workshop problems, reading background material provided and in text books.

### Opportunities for Formative Feedback

Workshops, and follow-ups.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment Assignment Assignment 15.00 Assignment Assignment 15.00 Total percentage (Assessment Coursework) 30.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 48 hr 00 mins 70.00 Total percentage (Assessment Exams) 70.00

Students will have to complete an online assessment at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound. The assessment will not take 48 hours to complete, but students will have a 48 hour time period in which to complete it. Students must submit a reasonable attempt at all assessments for this module to pass this module.