Space-time Geometry And General Relativity

Module description

 

Aims and objectives:
The aim of the course is to show how the concept of a four-dimensional manifold provides an appropriate model for space-time, with the geometric notions of metric and curvature leading to Einstein's general theory of relativity, a geometric theory of gravity. The course develops differential geometry to include tensor calculus and covariant differentiation, as well as solutions to Einstein's field equations.

 

Syllabus:
Equivalence principle, and the implications of formulating physics with no preferred inertial frames; Introduction to geometry; Embedded surfaces; Lengths of curves and geodesics, parallel transport; Tensors, particularly metric tensor; Covariant differentiation. Covariant differentiation and the Riemann curvature; parallel transport and geodesics. The Bianchi identities & the Einstein tensor; Equivalence principle and local Lorentz frames. Static and stationary fields, and their metric; Schwarzschild solution and its analysis; Introduction to Gravitational waves. Possibly: Introduction to cosmology. 

Formative Assessment

There are exercises included in the course notes and you will be set a selection of questions each week. Complete solutions will be made available. It is crucial that your work through these problems on your own. These exercises form an integral part of the course, and some of the examinable material will only be covered in the exercises.

 

 Indicative reading list - link to Leganto system where you can search with module code for lists

Prerequisites

6CCM331A Special Relativity and Electromagnetism

You cannot take this module with 6CCP3630 General Relativity and Cosmology

Assessment details

Written examination

Teaching pattern

Three hours of lectures each week and one hour of tutorials

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.