Course Materials
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- Lecturer: Profile: Christopher Couzens
Course information
General Prerequisites:
C7.5 General Relativity I
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Weight: 1
Course Level: M
Assessment Type: Written Examination
Course Overview:
In this, the second course in General Relativity, we have two principal aims. We first aim to increase our mathematical understanding of the theory of relativity and our technical ability to solve problems in it. We apply the theory to a wider class of physical situations, including gravitational waves and black hole solutions. Orbits in the Schwarzschild solution are given a unified treatment which allows a simple account of the three classical tests of Einstein's theory. This leads to a greater understanding of the Schwarzschild solution and an introduction to its rotating counterpart, the Kerr solution. We analyse the extensions of the Schwarzschild solution show how the theory of black holes emerges and exposes the radical consequences of Einstein's theory for space-time structure.
Learning Outcomes:
By the end of the course, students will be able to
Carry out tensor computations on Lorentzian manifolds
Use the linearised Einstein equations to solve problems in the weak gravitational regime
Construct the Penrose diagrams of Minkowski space-time, Schwarzschild, and the other simple spherically symmetric space-times
Explain the concept of the black hole and identify its mass and angular momentum
Carry out tensor computations on Lorentzian manifolds
Use the linearised Einstein equations to solve problems in the weak gravitational regime
Construct the Penrose diagrams of Minkowski space-time, Schwarzschild, and the other simple spherically symmetric space-times
Explain the concept of the black hole and identify its mass and angular momentum
Course Synopsis:
Mathematical background, the Lie derivative and isometries. The Einstein field equations with matter; the energy-momentum tensor for a perfect fluid; equations of motion from the conservation law. Linearised general relativity and the metric of an isolated body. Motion on a weak gravitational field and gravitational waves. The Schwarzschild solution and its extensions; Eddington-Finkelstein coordinates and the Kruskal extension. Penrose diagrams and the area theorem. Stationary, axisymmetric metrics and orthogonal transitivity; the Kerr solution and its properties; interpretation as rotating black hole.
Section outline
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These are the course lecture notes. They will be updated as the course progresses.
If you see any typos, or have confusions please email me.
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Problem sheet 1. Topics include Lie Derivative, Cold stars, null geodesics and Penrose diagrams
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Problem sheet 2. Contains computations on the Kerr black hole, Komar integrals and sketching manifolds from a given metric.
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Problem sheet 3. Surface gravity, Killing tensors, supercharging a Reissner--Nordstrom black hole.
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These are some old lecture notes from previous years. There is some overlap between the two courses but also some material which is new in the current course. Feel free to make use of these if you want.
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