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Module

PHY8043 : General Relativity

  • Offered for Year: 2020/21
  • Module Leader(s): Dr Gerasimos Rigopoulos
  • Lecturer: Dr Cora Uhlemann
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0

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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture91:009:00Present in Person (S2)
Scheduled Learning And Teaching ActivitiesLecture91:009:00Synchronous On-Line Material
Structured Guided LearningLecture materials361:0036:00Non-Synchronous Activities
Guided Independent StudyAssessment preparation and completion301:0030:00N/A
Structured Guided LearningStructured non-synchronous discussion181:0018:00N/A
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study941:0094:00N/A
Total200:00
Jointly Taught With
Code Title
MAS8811General Relativity
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A70Alternative assessment - class test
Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M10Written exercises 1
Written exercise2M20Written exercises 2
Assessment Rationale And Relationship

A substantial formal examination is appropriate for the assessment of the material in this module. The course assessments will consist of five assignments of approximately equal weight and will 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