Module: Advanced GR 2: Black Holes

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Advanced GR 2: Black Holes
Module Code	MTH1006 (ITS: MS540)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	9	Credit Rating	5

Description

This module covers both classical and quantum aspects of black holes. Topics include the no-hair conjecture, black hole formation, laws of black hole mechanics, Hawking radiation and black hole thermodynamics, black hole evaporation and the information loss 'paradox'.

Learning Outcomes

1. Analyze geodesics, construct maximal analytic extensions and construct Penrose diagrams for a number of important black hole spacetimes.
2. Derive a simple model for stellar interiors and a simple model for black hole formation.
3. Demonstrate an understanding of the no-hair conjecture, including proving basic uniqueness theorems.
4. Derive the laws of black hole mechanics.
5. Demonstrate that the laws of black hole mechanics are equivalent to the laws of thermodynamics when quantum mechanical effects are considered.
6. Construct the Penrose diagram for an evaporating black hole and discuss the information loss 'paradox' and its possible resolutions.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	No Description
Laboratory	3	Mathematica Lab
Seminars	3	Students must attend at least 3 seminars organized by the Centre for Astrophysics and Relativity.
Tutorial	12	No Description
Independent Study	83	No Description
Total Workload: 125

Section Breakdown
CRN	20046	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Peter Taylor	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Project	Mini-Project on solving geodesic equations and representing solutions in black hole spacetimes using Mathematica.	10%	n/a
Assignment	3 Sets of Homework Problems	30%	n/a
Formal Examination	n/a	60%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Black Hole Solutions
Schwarzschild, Kerr, Reissner-Nordstrom and Majumdar-Papapetrou spacetimes. Maximal extensions. Penrose diagrams. Geodesics and orbits in black hole spacetimes.

Black Hole Formation
Stellar interior solutions. Simple gravitational collapse models. Oppenheimer-Snyder collapse model.

Black Hole Uniqueness
No-Hair Conjecture. Uniqueness theorem for static black holes. Uniqueness theorem for stationary black holes.

Black Hole Mechanics
Laws of Black Hole Mechanics. Energy conditions. Hawking's Area Theorem.

Black Hole Thermodynamics
Quantum physics of black holes. The Hawking effects. Laws of Black Hole Thermodynamics. Black hole entropy. Black hole evaporation. Penrose diagram for an evaporating black hole. The Information Loss 'Paradox'.

Indicative Reading List

Books:

Valeri P. Frolov and Igor D. Novikov: 1998, Black Hole Physics, Springer, 978-079235145
Robert M. Wald: 1984, General Relativity, University of Chicago Press, 978-022687033
Eric Poisson: 2008, A Relativist's Toolkit, Cambridge University Press, 978-052153780

Articles:
None

Other Resources

None