Module: Advanced GR 2: Black Holes

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Advanced GR 2: Black Holes
Module Code	MS540
School	School of Mathematical Sciences
Module Co-ordinator	Semester 1: Peter Taylor Semester 2: Peter Taylor Autumn: Peter Taylor
Module Teacher	No Teacher Assigned
NFQ level	9	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
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

Programme or List of Programmes

MSAR	MSc in Astrophysics and Relativity

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