Course Materials
Main content blocks
- 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:
This course will further extend our understanding of general relativity. We begin by studying linearised gravity and gravitational waves before studying stellar collapse of cold stars and the inevitability of the formation of black holes.
We discuss singularities, the causal structure of spacetime using Penrose diagrams and give a formal definition of a black hole. We then study larger classes of black hole solutions including the Kerr--Newman and Reissner--Nordstrom solutions and study their causal properties before studying the laws of black hole thermodynamics.
We discuss singularities, the causal structure of spacetime using Penrose diagrams and give a formal definition of a black hole. We then study larger classes of black hole solutions including the Kerr--Newman and Reissner--Nordstrom solutions and study their causal properties before studying the laws of black hole thermodynamics.
Learning outcomes:
By the end of the course, students will be able to
- Understand linearised gravity and gravitational waves.
- Understand the gravitational collapse of a star to form a black hole.
- Understand the causal properties of various different spacetimes by constructing Penrose diagrams.
- Explain the concept of a black hole and identify its mass, angular momentum and electric and magnetic charges.
- Understand the laws of black hole thermodynamics and the need for a theory of quantum gravity.
Course synopsis:
Linearised gravity and gravitational waves. The Tolman--Oppenheimer--Volkoff equations and stellar collapse. Definition of a black hole and Penrose singularity theorems. Causality of spacetime and Penrose diagrams. Charged and rotating black holes. Laws of black holes thermodynamics and the Hawking temperature.
Section outline
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Opens: Wednesday, 20 January 2027, 5:12 PMDue: Monday, 1 February 2027, 11:59 PM
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Due: Tuesday, 2 March 2027, 11:59 PMProblem sheet 3. Surface gravity, Killing tensors, supercharging a Reissner--Nordstrom black hole.
DUE DATE: 2nd March 23:59
Sheets will be marked but do not contribute to your grade. -
Problem sheet 4. Entropy, and black hole thermodynamics.
This will not be marked.