PHYS 516 Spring 2025
PHYS 516 :: Physics Illinois :: University of Illinois at Urbana-Champaign
Course Schedule
Lectures will take place on Tuesdays and Thursdays from 12:30 - 13:50 h Central US in 276 Loomis Laboratory.
For details on semester dates, registration deadlines, etc., please check the Academic Calendar.
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The topics covered are the following:
- Formulations of General Relativity
- Lagrangian formulation
- Mathematical sidetrack A: Hypersurfaces
- 3+1 decomposition
- Hamiltonian formulation
- Mathematical sidetrack B: Congruences
- Lagrangian formulation
- Black hole theory
- Stationary and spherically symmetric black holes
- Horizons: event, apparent, and Killing
- Stationary and axisymmetric black holes
- Energy and angular momentum, Smarr's formula and the variation law
- Mathematical sidetrack C: Horizon generators
- General black holes and the laws of black hole mechanics
- Black hole perturbation theory
- Kerr geodesics
- Semi-relativistic approximation and the self-force
- Schwarzschild and Kerr black hole perturbation theory
In the table below, "MS" stands for "Mathematical sidetrack." Lecture notes will be available for download before each lecture.
In the column "Text suggestions" you will find:
- "P:X.Y" stands for Chapter X, Section Y, from the E. Poisson's textbook.
- "W:X.Y" stands for Chapter X, Section Y, from the R. M. Wald's textbook.
- "SM" stands for "Supplemental Material". These will often be "leisure reading" material that complements our course.
| Week | Date | Lectures | Homework | Text suggestions | |
|---|---|---|---|---|---|
| 1 |
Tuesday
01/21/2025 |
Welcome and Lecture 1 Lagrangian formulation Lect. Notes 01 |
P:4.1.1 to P:4.1.3 | ||
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Thursday
01/23/2025 |
Lecture 2 Lagrangian formulation (MS A: Hypersurfaces) Lect. Notes 02 |
P:1.7 and P:3.1, 3.2, 3.3, and 3.4.1 to 3.4.2 | |||
| 2 |
Tuesday
01/28/2025 |
Lecture 3 Lagrangian formulation (MS A: Hypersurfaces) Lect. Notes 03 |
HW 01 (due Feb. 06) |
P:1.4, P:3.4.3, and P:4.1.3 to 4:1:8 |
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Thursday
01/30/2025 |
Lecture 4 Lagrangian formulation Lect. Notes 04 |
P:4.1.3 to 4:1:8. SM: Corry et al. "Belated Decision in the Hilbert-Einstein Priority Dispute" (1997) |
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| 3 |
Tuesday
02/04/2025 |
Lecture 5 3+1 decomposition Lect. Notes 05 |
P4:1:8. then W:10 (Introduction), P:3.6.1, 4.2.2, and 3.5.1. | ||
|
Thursday
02/06/2025 |
Lecture 6 3+1 decomposition Lect. Notes 06 |
P4.2.2 and 3.5.1. SM: Ringstrom, "Origins and development of the Cauchy problem in general relativity" (2015) |
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| 4 |
Tuesday
02/11/2025 |
Lecture 7 3+1 decomposition Lect. Notes 07 |
P3.5.1, P3.6.1 to 3.6.4, and 3.6.7. SM: "Ripples from chasm" (Numerical relativity at Illinois in the 90s). (6 mins long) |
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Thursday
02/13/2025 |
Lecture 8 3+1 decomposition |
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| 5 |
Tuesday
02/18/2025 |
Lecture 9 Hamiltonian formulation Lect. Notes 09 |
HW 02 (due Mar. 04) |
P3.5.3, P4.2.1, P4.2.3, and P4.2.4 SM: Deser, "The legacy of ADM" (2015) |
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|
Thursday
02/20/2025 |
Lecture 10 Hamiltonian formulation Lect. Notes 10 |
P4.2.4 and P4.2.5 | |||
| 6 |
Tuesday
02/25/2025 |
Lecture 11 Hamiltonian formulation |
P4.2.4 and P4.2.5 | ||
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Thursday
02/27/2025 |
Lecture 12 MS B: Congruences |
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| 7 |
Tuesday
03/04/2025 |
Lecture 13 Stationary and spherically symmetric black holes |
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Thursday
03/06/2025 |
Lecture 14 Horizons: event, apparent, and Killing |
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| 8 |
Tuesday
03/11/2025 |
Lecture 15 Stationary and axisymmetric black holes |
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Thursday
03/13/2025 |
Lecture 16 Stationary and axisymmetric black holes |
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| 9 |
Tuesday
03/18/2025 |
Spring break (no class) |
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Thursday
03/20/2025 |
Spring break (no class) |
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| 10 |
Tuesday
03/25/2025 |
Lecture 17 Stationary and axisymmetric black holes |
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Thursday
03/27/2025 |
Lecture 18 Energy and angular momentum, Smarr's formula, and the variation law |
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| 11 |
Tuesday
04/01/2025 |
Lecture 19 Energy and angular momentum, Smarr's formula, and the variation law |
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Thursday
04/03/2025 |
Lecture 20 Energy and angular momentum, Smarr's formula, and the variation law |
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| 12 |
Tuesday
04/08/2025 |
Lecture 21 General black holes and their mechanics |
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Thursday
04/10/2025 |
Lecture 22 General black holes and their mechanics |
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| 13 |
Tuesday
04/15/2025 |
Lecture 23 General black holes and their mechanics |
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Thursday
04/17/2025 |
Lecture 24 General black holes and their mechanics |
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| 14 |
Tuesday
04/22/2025 |
Lecture 25 Kerr geodesics |
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Thursday
04/24/2025 |
Lecture 26 Semirelativistic approximation and the self-force |
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| 15 |
Tuesday
04/29/2025 |
Lecture 27 Black hole perturbation theory |
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Thursday
05/01/2025 |
Lecture 28 Black hole perturbation theory |
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| 16 |
Tuesday
05/06/2025 |
Lecture 29 Black hole perturbation theory |
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Thursday
05/08/2025 |
Lecture 30 Black hole perturbation theory |
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| Final exams' week 05/09/2025 - 05/15/2025 |
Takehome final exam: TBA |
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