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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-ordinatorSemester 1: Peter Taylor
Semester 2: Peter Taylor
Autumn: Peter Taylor
Module TeacherNo Teacher Assigned
NFQ level 9 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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.

Workload Full-time hours per semester
Type Hours Description
Lecture24No Description
Laboratory3Mathematica Lab
Seminars3Students must attend at least 3 seminars organized by the Centre for Astrophysics and Relativity.
Tutorial12No Description
Independent Study83No 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 Assessment40% Examination Weight60%
Course Work Breakdown
TypeDescription% of totalAssessment Date
ProjectMini-Project on solving geodesic equations and representing solutions in black hole spacetimes using Mathematica.10%n/a
Assignment3 Sets of Homework Problems30%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

Programme or List of Programmes
MSARMSc in Astrophysics and Relativity

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