Description

Black holes are fascinating astrophysical objects from which light cannot escape. Their description within Einstein's General Theory of Relativity led Hawking and others (Bekenstein, Bardeen, Carter, Israel) to conclude that black holes obey the laws of thermodynamics. In particular, they attached a well-defined thermodynamic meaning to geometric characteristics of black holes such as their area and surface gravity. Later on, Hawking demonstrated that when quantum mechanical effects are taken into account, black holes radiate in exactly the same way as a black body would.

In this project students will learn about black holes and explore different aspects of their properties. Possible directions include Black Hole Mechanics, Hawking Radiation, causal structure, and the Membrane Paradigm.

Mode of Operation and Evidence of Learning

The project will run primarily through guided independent reading, regular meetings with the supervisor, problem solving, and discussion of the relevant physical and mathematical ideas. Students will be expected to read from textbooks and lecture notes, work through selected derivations and examples, and gradually develop ownership of a more specialised aspect of the topic.

Evidence of learning may include explaining key ideas and derivations during meetings, discussing the physical interpretation of important results, presenting worked examples, and producing written project work that demonstrates understanding of both the underlying geometric framework and the specific black-hole phenomena studied.

Prerequisites:

• MATH2741 Methods of Mathematical Physics II

Co-requisites:

• MATH4051 General Relativity IV
• MATH4231 Statistical Mechanics IV (recommended but not required)

Resources:

• For a brief introduction to the concepts see the Wiki pages
• One of the best textbooks in GR is General Relativity by R. Wald
• Another (slightly less mathematical) textbook is Spacetime and Geometry by S. Carroll
• An excellent set of notes on Black Holes by P. Townsend