Module: Advanced GR 2: Black Holes

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Advanced GR 2: Black Holes
Module Code	MS540 (ITS) / MTH1006 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Peter Taylor
Module Teachers	-
NFQ level	9	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None

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

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'.

Assessment Breakdown
Continuous Assessment	40%	Examination Weight	60%

Type	Description	% of total	Assessment Date
Course Work 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

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

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

Other Resources

None