The University of Southampton

MATH3006 Relativity, Blackholes and Cosmology

Module Overview

This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is currently the subject of enthusiastic study from the theoretical and experimental standpoints. The module starts by introducing the special theory of relativity in a manner designed to make the transition to the general theory more tractable. In addition, in order to understand the general theory fully, some familiarity with tensor calculus is required. This will involve some self-study material at the start of the module. The rest of the module will be devoted to a detailed investigation of the theory itself together with applications to classical black holes and cosmology. The theory is full of surprises and challenging new ideas and the module is designed to make these accessible to students from a wide variety of backgrounds.

Aims and Objectives

Module Aims

• To understand the mathematical and physical basis of Einstein's special theory of relativity • To explore the properties of black holes • To understand the basis of relativistic cosmology and study the basic cosmological models • To appreciate the nature of tensor calculus and its role in the theory.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Draw diagrams to explain many of the key properties of these solutions
  • Understand the physical principles which guided Einstein to the theory of relativity
  • Solve Einstein's equations in a variety of simple situations
  • Manipulate tensors in a competent manner
  • Investigate the geodesic structure of the most important solutions of the theory
  • Derive the basic results in cosmology
  • Appreciate the experimental status of the theory and derive the classic tests
  • Understand the key properties of black holes


Introduction to tensors Tensor algebra Tensor calculus Special Relativity The key attributes of special relativity The elements of relativistic mechanics The principles of general relativity Mach's principle The principle of equivalence The principle of general covariance The simplicity principle The correspondence principle The field equations of general relativity The lift experiments The Newtonian correspondence The energy-momentum tensor Experimental tests of general relativity The Schwarzschild solution The four classic tests Classical black holes Non-rotating black holes Charged black holes Rotating black holes Cosmology Newtonian cosmology Relativistic cosmology Hubble's law Classification and properties of Friedmann models

Learning and Teaching

Teaching and learning methods

Lectures, tutorials, private study

Independent Study90
Total study time150

Resources & Reading list

Schutz B.F, A. First Course in General Relativity. 



MethodPercentage contribution
Coursework 20%
Written exam 80%


MethodPercentage contribution
Exam 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisite: MATH2038 Partial Differential Equations 2016-17 For Physics students, the prerequisites are MATH1006 Mathematical Methods For Physical Scientists 1a 2016-17, MATH1007 Mathematical Methods For Physical Scientists 1b 2016-17 and MATH2015 Mathematical Methods For Scientists 2016-17 instead.


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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