To give the student a clear understanding of where Newtonian Mechanics breaks down.  To introduce the student to the principles and the basic formalism of General Relativity.  To apply these ideas to present cosmological models and give the student a sound understanding of these models and their limitations.  To acquaint the students with the latest questions confronting cosmologists.

At the end of this module the student should be able to demonstrate a firm understanding of the short-comings in the Newtonian theory of gravity, the problem of defining inertial frames, and the reasons why Special relativity fails to resolve these issues.  The student should be able to understand the concept of tensors and manipulate simple tensorial equations, understand the elements of differential geometry in relation to describing curved spaces.  The student will be familiar with the Einstein field equations which describe the gravitational field arising from any distribution of matter, and be able to analyse the motion of observers around a central mass point.  The student will be able to analyse the key tests of general relativity and show how the predictions of this theory deviate from Newtonian theory.  Finally, the student should be able to describe the behaviour of observers in the vicinity of a black hole which has no charge or rotation.

The student will be able to describe the cosmological principle and explain why it is so central to our ability to model the Universe.  They will be able to describe the evolution of the standard model and derive the fundamental parameters that determine the cosmic evolution.  The student should be able to describe how these parameters are estimated from observations and why the standard model cannot explain all the observations.  They should be able to describe inflationary models of the universe, and explain how they resolve the conflicts with observation. Finally, the student should be able to describe the origin and early evolution of the universe as understood from strong theory, particle physics and the physics of phase transitions.

This module introduces the student to the ideas and formalism of General Relativity.  Beginning with the Principle of Equivalence, it goes on to look at some of the solutions of Einstein's field equations and their applications in cosmology.  This should also give the student an understanding of contemporary ideas and problems associated with the Standard Big Bang Model of the Universe.

Introduction (2 lectures)

Inadequacy of Newtonian Gravity

Inadequacy of Special Relativity

Mach's Principle

Einstein's Principle of Equivalence

The Mathematics of General Relativity (4 lectures)

Tensors and Manifolds

Riemannian Space

Geodesics and Curved Spacetime

Tensor Calculus

The Principles of General Relativity (4 lectures)

Einstein's Field Equations

The Field Equations in the Presence of Matter

The Schwarzchild Solution

Classical tests of General Relativity

Black Holes

Cosmology (8 lectures)

The Cosmological Principles

The Robertson-Walker metric

The Friedmann Models

Matter-radiation coupling

Inflationary models

The case for dark matter and energy

24 hours of lectures and tutorial classes.

i.                Foster and Nightingale, General Relativity, Springer-Verlag.

ii.              Liddle, A, An Introduction to Modern Cosmology, Wiley.

iii.             M Berry, Principles of Cosmology and Gravitation, Cambridge University Press.

iv.            Rindler, Essential Relativity, Van Nostrand Reinhold Co.

v.              Rowan-Robinson, Cosmology, Clarendon Press, Oxford .