PHYM006 
Relativity and Cosmology 
202223 

Prof. T.J. Harries 


Delivery Weeks: 
T2:0111 

Level: 
7 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
32 students (approx) 

Description
This module is an introduction a cornerstone of 20th century physics,
the general theory of relativity, Einstein's geometric theory of
gravity. The module begins with a recap of special relativity.
Subsequently, the mathematical tools (tensor analysis and differential
geometry) that underpin general relativity are presented, and students
will require a good level level of mathematical fluency and intuition in
order to engage with material. Topics include Einstein's field equation,
Schwarzschild's solution and black holes, gravitational waves, and the
RobertsonWalker metric and cosmology.
Module Aims
The module aims to develop an understanding of Einstein's theory of
general relativity (GR). The module starts with a recap of special
relativity and then introduces the principles of equivalence, covariance
and consistency that lead Einstein to the general theory. The
mathematics of tensors and differential geometry are presented in the
context of Einstein's field equation. This is followed by a detailed
derivation of Schwarzchild's solution and its implication for time and
space around a black hole. The module concludes by examining the use of
GR in cosmology.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 give coherent explanations of the principles associated with:
special relativity, general relativity, and cosmology;
 interpret observational data in terms of the standard
model of the evolution of the Universe;
 describe experiments and observational evidence to test the
general theory of relativity, explain how these support the
general theory and can be used to criticise and ruleout
alternative possibilities;
 apply tensors to the description of curved spaces;
 solve problems by applying the principles of relativity;
 deduce the Friedmann equations describing the evolution of the Universe.
 explain what is meant by: intrinsic and extrinsic curvatures,
the curvature of space, local inertial reference frame, and
Riemannian coordinates/geometry;
 describe world lines of particles and photons in a curved spacetime;
 describe the cosmological principle and the RobertsonWalker metric;

Discipline Specific Skills and Knowledge:
 explain to nonspecialists the basis of one of the cornerstones
of 20th century physics;

Personal and Key Transferable / Employment Skills and Knowledge:
 locate, retrieve and evaluate relevant information from the WWW;
 meet deadlines for completion of work to be discussed in
class by developing appropriate timemanagement strategies.
Syllabus Plan

Introduction

Recap of key aspects of special relativity
 Galilean and Lorentz transformations
 Length contraction and time dilation
 Doppler effect
 Relativistic mechanics

Tensor analysis
 Covariant and contravariant tensors
 Reciprocal basis vectors
 Tensor algebra
 The metric tensor
 Christoffel symbols and covariant differentiation
 The geodesic equation

Curved spaces
 Intrinsic and extrinsic curvature
 Parallel transport
 Riemannian curvature
 Ricci tensor and scalar

Einstein's field equation
 The stressenergy tensor
 Einstein's field equation
 The weak field limit
 Schwarzschild's solution
 Black holes and singularities

Black holes
 Geodesic equations, orbital shape equation
 Falling into a black hole
 EddingtonFinkelstein coordinates
 Rotating black holes and the Kerr metric
 Frame dragging and ergosphere

Gravitational waves
 Linearised gravity
 Wave equation
 Weak gravitational waves
 The motion of a test particle
 Detecting gravitational waves

Cosmology
 The cosmological principle
 RobertsonWalker metric
 Redshift distance relation
 The Friedmann equations
 Inflation

Additional Topics
 Eotvos experiments
 Observational tests of GR
 A recap of special relativity
 An introduction to tensor mathematics
 Derivation of the Friedmann equations from the RobertsonWalker metric
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
82 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
112 
Discussion in class 
0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
112 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
May/June 
112 
Mark via MyExeter, collective feedback via ELE and solutions. 
Resources
The following list is offered as an indication of the type & level of information that
students are expected to consult. Further guidance will be provided by the Module Instructor(s).
Core text:
Supplementary texts:
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Vector Mechanics (PHY1021), Introduction to Astrophysics (PHY1022) and Mathematics with Physical Applications (PHY2025) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
112 
August/September assessment period 
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods 
SLT  scheduled learning & teaching activities 
22 hrs 
GIS  guided independent study 
128 hrs 
PLS  placement/study abroad 
0 hrs 
Total 
150 hrs 


Summative assessment 
Coursework 
0% 
Written exams 
100% 
Practical exams 
0% 
Total 
100% 

Miscellaneous
IoP Accreditation Checklist 
 N/A this is an optional module

Availability 
MPhys only 
Distance learning 
NO 
Keywords 
Physics; Theory; Spaces; Curvature; Time; Curves; General theory; Shifts; Cosmological; Equation; Inertial frame. 
Created 
01Oct10 
Revised 
27Jun19 