The University of Southampton
Courses

# 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:

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

### Syllabus

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

TypeHours
Teaching60
Independent Study90
Total study time150

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

### Assessment

#### Summative

MethodPercentage contribution
Coursework 20%
Written exam 80%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

For Physics students, the prerequisites are MATH1006, MATH1007 and MATH2015 instead of MATH2038.

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
MATH2038Partial Differential Equations

### Costs

#### 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 www.calendar.soton.ac.uk.