PX43615 General Relativity
Introductory description
Einstein's general theory of relativity (GR) is the basis for our understanding of black holes and the Universe on its largest scales. In GR the Newtonian concept of a gravitational force is abolished, to be replaced by a new notion, that of the curvature of spacetime. This leads in turn to predictions of phenomena such as the bending of light and gravitational time dilation that are well tested, and others, such as gravitational waves, which have only recently been directly detected.
The module starts with a recap of Special Relativity, emphasizing its geometrical significance. The formalism of curved coordinate systems is then developed. Einstein's equivalence principle is used to link the two to arrive at the field equations of GR. The remainder of the module looks at the application of general relativity to stellar collapse, neutron stars and blackholes, gravitational waves, including their detection, and finally to cosmology where the origin of the "cosmological constant"  nowadays called "dark energy"  becomes apparent.
Module aims
To present the theory of General Relativity and its applications in modern astrophysics, and to give an understanding of blackholes
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
The geometry of spacetime and the invariant “interval” in special relativity; geodesics and equations of motion applied to circular orbits within the Schwarzschild metric; 4vector formulation of special relativity; metric of special relativity; the equivalence principle and local inertial frames; motivation for considering curved spacetime; vectors and tensors in curved coordinate systems; geodesic motion revisited; motion in almostflat spacetime: the Newtonian limit; the curvature and stressenergy tensors; how the metric is determined: Einstein's field equations; Schwarzschild metric; observable consequences; blackholes; stability of orbits; extraction of energy; gravitational radiation and its detection; cosmology: the RobertsonWalker metric
Learning outcomes
By the end of the module, students should be able to:
 Explain the metric nature of special and general relativity, how the metric determines the motion of particles
 Undertake calculations involving the Schwarzschild metric
 Describe features of blackholes
 Demonstrate knowledge of current attempts to detect gravitational waves
Indicative reading list
BF Schutz A first course in general relativity, Cambridge University Press,
M.P Hobson, G. Efstathiou, A.N. Lasenby, General Relativity  An Introduction for Physicists, CUP,
L. D. Landau, E. M. Lifshit︠s︡, The Classical Theory of Fields
View reading list on Talis Aspire
Interdisciplinary
The theory of General Relativity, like quantum theory, has been the result of collaboration between people working in physics and in mathematics with insights flowing in both directions. At its core is a simple hypothesis about observations (the equivalence principle), which leads to a theory of gravity based on the differential geometry of curved spaces. This module covers the necessary mathematics and computes some of the consequences of the theory for the physical Universe.
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Seminars  (0%) 
Private study  120 hours (80%) 
Total  150 hours 
Private study description
Self study
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B2
Weighting  Study time  Eligible for selfcertification  

Inperson Examination  100%  No  
Answer 3 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Optional for:

TMAAG1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 1 of TMAAG1P0 Postgraduate Taught Mathematics
 Year 1 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
 Year 4 of UPXAF303 Undergraduate Physics (MPhys)
This module is Option list A for:
 Year 1 of TMAAG1P0 Postgraduate Taught Mathematics
 Year 3 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 3 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list B for:
 Year 4 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 4 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
This module is Option list C for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 4 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe