Description

Black holes are one of the most interesting objects that have emerged from Einstein’s General theory of Relativity. They are defined as regions of spacetime where spacetime itself is so distorted that not even light can escape from them; this is what makes them appear ‘black’. 

This project consists of three parts. The first part of the project explores the basic concepts of General relativity. The second part elaborates on the simplest black hole solution, namely the Schwarzschild black hole. In particular, the geometric invariants are computed in several different coordinate systems, as well as other relevant quantities like the surface gravity and the area of the black hole horizon. For the final part of the project, you can choose one of the following options:

1. Study the trajectories of massive and massless particles around the Schwarzschild black hole. You may find instructive to write a short code to solve the geodesic equation and experiment with various initial conditions.
2. Compute the so called ‘Quasinormal modes’ of the black hole, which describe how the black hole returns to equilibrium when something falls in it. This will require some coding (in whichever programming language you prefer).
3. Study black hole thermodynamics. One of the most important contributions of Stephen Hawking is that he realised that black holes have a temperature and entropy associated with their event horizon and they obey the laws of thermodynamics, much like a pot of boiling water.  

Other types of black holes, for example charged ones, or in higher dimensions can also be explored.

Prerequisites:

• Mathematical Physics II 

Co-requisites:

• Statistical Mechanics III 

Resources:

Popular/Historical:  

• K.S. Thorne, Black Holes and Time Warps, Picador, 1994.
• W. Israel, Dark Stars: The Evolution of an Idea, in Three Hundred Years of Gravitation (S.W. Hawking & W. Israel, eds.), Cambridge University Press, 1987. 

Textbooks: 

• S.W. Hawking & G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973. 
• R.M. Wald, General Relativity, Chicago University Press, 1984. 
• S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, 2004. 

Lecture Notes: 

• P. Townsend, Black Holes. Available online at arXiv:gr-qc/9707012.
• F. Dowker, Black Holes. Available online here

https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/theoretical-physics/msc/current/black-holes/bh-notes-2014_15.pdf