Mathematics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

## MATH4GR Introduction to General Relativity

 First Semester
10 points

This module is an introduction to General Relativity, the theory of gravity by Albert Einstein. Building on the module Differential Geometry (MATH4DG), which takes place in the first half of semester 1, we develop Einstein’s idea that “space” and “time” form a continuum “spacetime” described by a 4-dimensional Lorentzian manifold. The module begins with Special Relativity, which applies to physical systems for which gravity is negligible in comparison to other forces. The spacetime of interest here is the flat (non-curved) Minkowski space. The idea is now to describe a general physical system in terms of general curved spacetimes. The curvature of the Lorentzian manifolds, which represent the spacetimes, is then interpreted as gravity.

Einstein found an analogue to the Poisson equation, which in Newtonian gravity describes the relation between the mass density of the matter fields and the gravitational field: Einstein’s field equations — the equations which govern the gravitational dynamics. In this module, we discuss the mathematical and physical ideas above in detail. Further topics are important classes of solutions of Einstein’s field equations, for example the Schwarzschild solution.

At Otago, we have a lively research group in this area, which includes Jörg Frauendiener, Jörg Hennig and Florian Beyer. Students should also consider the module MATH4AR Advanced Topics in General Relativity, which takes place in semester 2.

### Prerequisites

MATH4DG Differential Geometry, MATH306 is recommended

### Textbook

Hughston, Tod: An Introduction to General Relativity, (London Mathematical Society Student Texts),

Two copies of the book are on close reserve in the Science Library

### Lecturers

Jörg Frauendiener (phone 479-7770, email: joergf@maths.otago.ac.nz)

### Assessment

3 written assignments and a 30min oral exam

### Final mark

Your final mark F in the paper will be calculated according to this formula:

F = 0.5A + 0.5E

where:

• E is the Exam mark
• A is the Assignments mark

and all quantities are expressed as percentages.

### Students must abide by the University’s Academic Integrity Policy

Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.

The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.

Plagiarism is defined as:

• Copying or paraphrasing another person’s work and presenting it as your own.
• Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
• Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
• Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.

All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.