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2010/1 Module Catalogue
Module Provider: Physics Short Name: PH3-GRC
Level: HE3 Module Co-ordinator: PALMER PL Dr (Elec Eng)
Number of credits: 10 Number of ECTS credits: 5
Module Availability

Module Availability:


Semester 2


Assessment Pattern

Unit(s) of Assessment


Weighting Towards Module Mark( %)


Examination (End of semester)




Qualifying Condition(s) 


University general regulations refer.


Module Overview



Module Aims

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.


Learning Outcomes

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.


Module Content

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


Methods of Teaching/Learning

24 hours of lectures and tutorial classes.


Selected Texts/Journals

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 .


Last Updated

August 2010.