• Offered for Year: 2024/25

• Module Leader(s): Dr Gerasimos Rigopoulos
• Lecturer: Dr Adam Ingram

• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus

Semesters

Your programme is made up of credits, the total differs on programme to programme.

Aims

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

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 Lorentzian 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, freely falling frames. Applications of the mathematics to general relativity; spherically symmetric solutions to the Einstein equations; Light bending, perihelion precession, Schwarzschild solution, Black holes (with a heuristic demonstration of Hawking radiation, time permitting) and rudiments of cosmology and gravitational waves.

Teaching Methods

Teaching Activities

Jointly Taught With

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

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

Exams

Exam Pairings

Other Assessment

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

The coursework assignments 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

• PHY8043's Reading List

Timetable

• Timetable Website: www.ncl.ac.uk/timetable/
• PHY8043's Timetable