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
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
1	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
2	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)
3	Tuesday 02/04/2025	Lecture 5 3+1 decomposition Lect. Notes 05		P:4.1.8. then W:10 (Introduction), P:3.6.1, 4.2.2, and 3.5.1.
3	Thursday 02/06/2025	Lecture 6 3+1 decomposition Lect. Notes 06		P:4.2.2 and 3.5.1. SM: Ringstrom, "Origins and development of the Cauchy problem in general relativity" (2015)
4	Tuesday 02/11/2025	Lecture 7 3+1 decomposition Lect. Notes 07		P:3.5.1, P:3.6.1 to 3.6.4, and 3.6.7. SM: "Ripples from chasm" (Numerical relativity at Illinois in the 90s). (6 mins long)
4	Thursday 02/13/2025	Lecture 8 3+1 decomposition
5	Tuesday 02/18/2025	Lecture 9 Hamiltonian formulation Lect. Notes 09	HW 02 (due Mar. 04)	P:3.5.3, P:4.2.1, P:4.2.3, and P:4.2.4 SM: Deser, "The legacy of ADM" (2015)
5	Thursday 02/20/2025	Lecture 10 Hamiltonian formulation Lect. Notes 10		P:4.2.4 and P:4.2.5
6	Tuesday 02/25/2025	Lecture 11 Hamiltonian formulation Lect. Notes 11		P:4.2.4 and 4.2.5
6	Thursday 02/27/2025	Lecture 12 Hamiltonian formulation Lect. Notes 12		P:4.2.6 and 4.2.7 SM: Chandrasekhar, "The general theory of relativity: Why 'It is probably the most beautiful of all existing theories'" (1984)
7	Tuesday 03/04/2025	Lecture 13 Hamiltonian formulation Lect. Notes 13		P:4.2.6 and 4.2.7
7	Thursday 03/06/2025	Lecture 14 MS B: Congruences Lect. Notes 14		P:1.3, 1.5, 1.10, and 2.2
8	Tuesday 03/11/2025	Lecture 15 MS B: Congruences Lect. Notes 15	HW 03 (due Mar. 27)	P:2.3 and P:2.4
8	Thursday 03/13/2025	Lecture 16 MS B: Congruences / Black holes Lect. Notes 16		P:2.4 and P:5.1
9	Tuesday 03/18/2025	Spring break (no class)
9	Thursday 03/20/2025	Spring break (no class)
10	Tuesday 03/25/2025	Lecture 17 Schwarzschild black hole Lect. Notes 17		P:5.1
10	Thursday 03/27/2025	Lecture 18 Horizons: event, apparent, and Killing. Lect. Notes 18		P:5.1.6 to 5.1.10. SM: Matzner et al., "Geometry of a black hole collision'" (1995) SM: Thornburg, "Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity" (2007)
11	Tuesday 04/01/2025	Lecture 19 Mass and angular momentum. Lect. Notes 19	HW 04 (due Apr. 08)	P:4.2.9 and P:4.3.1 to 4.3.4
11	Thursday 04/03/2025	Lecture 20 Kerr black hole. Lect. Notes 20		P:5.3 SM: Kerr, "Discovering the Kerr and Kerr-Schild metrics" (2007) SM: Teukolsky, "The Kerr metric" (2015)
12	Tuesday 04/08/2025	Lecture 21 Kerr black hole. Lect. Notes 21		P:5.3 SM: Schirber, "Energy Boost from Black Holes" (2015)
12	Thursday 04/10/2025	Lecture 22 Kerr black hole. Lect. Notes 22	HW 05 (due Apr. 24)	P:5.3 and P:5.2.4 SM: Bardeen, Press, and Teukolsky, "Rotating black holes: locally nonrotating frames, energy extractions, and scalar synchrotron radiation" (1972)
13	Tuesday 04/15/2025	Lecture 23 Kerr black holes / General black holes and their mechanics Lect. Notes 23		P:5.3 and P:5.4
13	Thursday 04/17/2025	Lecture 24 General black holes and their mechanics Lect. Notes 24		P:5.5 SM: Bardeen, Carter, and Hawking, "The four laws of black hole mechanics" (1973)
14	Tuesday 04/22/2025	Lecture 25 General black holes and their mechanics Lect. Notes 25		P:5.5
14	Thursday 04/24/2025	Lecture 26 General black holes and their mechanics Lect. Notes 26 Black hole perturbation theory Notes	HW 06 (due May 6)	P:5.5 SM: Outreach article on the papers by Kehle and Unger
15	Tuesday 04/29/2025	Lecture 27 Black hole perturbation theory Notes		SM: Vishveshwara, "Scattering of Gravitational Radiation by a Schwarzschild Black-hole" (1970) SM: Schutz and Will, "Black hole normal modes: a semianalytical approach" (1985)
15	Thursday 05/01/2025	Lecture 28 Black hole perturbation theory Notes
16	Tuesday 05/06/2025	Lecture 29 Black hole perturbation theory Notes		SM: Davis, Ruffini, and Tiomno, "Pulses of Gravitational Radiation of a Particle Falling Radially into a Schwarzschild Black Hole" (1972)
16	Thursday 05/08/2025	--- ---
	Final exams' week 05/09/2025 - 05/15/2025	Takehome final exam: Exam