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Module

PHY8038 : General Relativity

  • Offered for Year: 2019/20
  • Module Leader(s): Dr Gerasimos Rigopoulos
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value: 15
ECTS Credits: 8.0

Aims

To introduce the basic ideas of Einstein’s theory of general relativity. To introduce a basic understanding of differential geometry needed for general relativity.

Module summary
Newton’s theory of gravity, based on the idea of a force of attraction between any two bodies, reigned supreme for about 250 years. In 1916 Einstein banished the notion of a gravitational force to the realms of history with his formulation of the theory of general relativity. This theory is based on the novel idea that the three dimensions of space and one dimension of time be treated as a unified 4-dimensional manifold called spacetime. The presence of matter bends spacetime from its flat Euclidean form, and what was thought of as the presence of an attractive force is now understood as the motion on this curved spacetime geometry. (Matter tells spacetime how to curve; spacetime tells matter how to move.)

The proper mathematical setting for Einstein’s theory of curved spacetime makes use of differential geometry. Because differential geometry plays an important role in other areas of mathematics and mathematical physics, we will spend the initial part of the course developing the necessary machinery in some detail. After encountering the needed mathematical ideas we will present the Einstein field equations, and then study some of the standard solutions. This will lead us into the study of black holes and the classic predictions of the theory of general relativity. We will stress how it is that Einstein’s theory makes different testable predictions from Newton’s theory of gravity.

Outline Of Syllabus

Definition of a manifold; tangent and cotangent spaces; vector and tensor fields; the connection, parallel transport, and covariant differentiation; the curvature tensor. Applications of the mathematics to general relativity; spherically symmetric solutions to the Einstein equations; Schwarzschild solution; perihelion precession, light bending, radar delay; black holes and Hawking radiation.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion12:302:30Unseen exam
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture341:0034:00Formal lectures
Guided Independent StudyAssessment preparation and completion11:201:20Written Examination
Guided Independent StudyAssessment preparation and completion118:0018:00Revision for unseen exam
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study148:1048:10Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study63:0018:00Review of coursework assignments and course test
Guided Independent StudyIndependent study64:0024:00Preparation for coursework assignments
Total150:00
Jointly Taught With
Code Title
MAS8853General Relativity
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Tutorials (within lectures) are used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1502A95N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8853General Relativity2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments are expected to consist of six written assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable