General Relativity - MAT00089M
Module summary
General Relativity (GR) is the extension of Einstein’s theory of Special Relativity to incorporate gravity, which is now understood as the effect of spacetime curvature rather than a force as such. This module will explain General Relativity and its mathematical background, i.e., the calculus of tensors on manifolds. Various applications and consequences of GR will be studied, including black holes, gravitational waves and cosmology. Developments in these areas have produced a number of Nobel Prizes in recent years.
Related modules
Additional information
An introduction to General Relativity, its mathematical underpinnings and physical applications. Elective/MSc students should have studied Lagrangian mechanics and special relativity and have a firm background in mathematics applied to physics, preferably including the use of index notation and tensors in special relativity or other branches of mechanics.
Pre-requisite modules:
Electromagnetism & Special Relativity (H) or Quantum Field Theory (M)
Classical Dynamics (I)
Vector & Complex Calculus (I)
Post-requisite modules:
Advanced Mathematical Physics
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 2 2023-24 |
Module aims
General Relativity (GR) is the extension of Einstein’s theory of Special Relativity to incorporate gravity, which is now understood as the effect of spacetime curvature rather than a force as such. This module will explain General Relativity and its mathematical background, i.e., the calculus of tensors on manifolds. Various applications and consequences of GR will be studied, including black holes, gravitational waves and cosmology. Developments in these areas have produced a number of Nobel Prizes in recent years.
Module learning outcomes
By the end of the module, students will be able to:
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Employ tensor calculus and index notation accurately;
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Solve unseen problems in General Relativity, including problems related to the geometry of curved manifolds, geodesics, tensor calculus and solutions of the Einstein equation;
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Interpret mathematical results concerning General Relativity in physical terms and vice versa.
Module content
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A brief survey of the Newtonian theory of gravitation and the reasons for generalising the theory of special relativity in order to account for gravity.
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An introduction to geometry of Riemannian and Lorentzian manifolds
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Tensors and the tensor calculus.
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The idea that the paths of free particles or light rays are time-like or null geodesics, respectively, in a curved space-time.
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The Einstein field equation and its Newtonian limit
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The Schwarzschild metric
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Gravitational waves
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Cosmology
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy
Indicative reading
SM Carroll, Spacetime and geometry: an introduction to general relativity
Cambridge University Press (U 0.11 CAR)
M Ludvigsen, General Relativity: a geometric approach, Cambridge University Press (S.82 LUD)
W Rindler, Essential relativity : special, general and cosmological, Springer (U 0.11 RIN)