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# General Relativity - MAT00089M

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• Department: Mathematics
• Module co-ordinator: Prof. Chris Fewster
• Credit value: 20 credits
• Credit level: M
• Academic year of delivery: 2023-24

## 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

• None

### Prohibited combinations

• None

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:

## Module will run

Occurrence Teaching cycle
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:

1. Employ tensor calculus and index notation accurately;

2. Solve unseen problems in General Relativity, including problems related to the geometry of curved manifolds, geodesics, tensor calculus and solutions of the Einstein equation;

3. Interpret mathematical results concerning General Relativity in physical terms and vice versa.

## Module content

• 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.

• An introduction to geometry of Riemannian and Lorentzian manifolds

• Tensors and the tensor calculus.

• The idea that the paths of free particles or light rays are time-like or null geodesics, respectively, in a curved space-time.

• The Einstein field equation and its Newtonian limit

• The Schwarzschild metric

• Gravitational waves

• Cosmology

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
General Relativity
3 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
General Relativity
3 hours 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