# MATH5515 Special Topics (Pure)

MATH5515 is a Honours and Postgraduate coursework Mathematics course. See the course overview below.

The special topic for Semester 1 2013 is - Mathematical Relativity.

Units of credit: 6

Prerequisites:

Cycle of offering: Variable

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH5515, you can log into UNSW Moodle for this course.

#### Course Overview

Passenger: "Excuse me, Herr Professor Einstein, but what time does the next station stop at this train?''

Relativity is the concept that motion and its effects on physical processes are relative, and cannot be measured absolutely. This course is intended to be a look at the mathematics of Relativity, as well as a little of its physics.

We will begin with Special Relativity (Einstein, 1905) which covers non-gravitational physics. Special Relativity will be considered from a mathematical viewpoint as an easy generalisation of linear algebra.

General Relativity (Einstein, 1915) is the theory of the gravitational field, and came out of an effort to incorporate gravity into the framework of Special Relativity. Its natural language is differential geometry, and we will spend some time covering or revising the geometry we need to state and use the theory.

Having done that, we will consider Space-Times, The Principles of General Relativity, and Einstein's equations. We follow this with a brief look at the symmetries admitted by solutions of Einstein's equations, which leads to the famous Schwarzschild solution for a non-rotating black hole. This solution is studied in some detail. If time permits we will look at other black hole solutions and their properties and maybe Gravitational Radiation.

We finish with Relativistic Cosmology: a study of the shape of the Universe as a whole.