PHY483/1483F

Pre-class reading and digitised lecture notes

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Canada License.
(CC) awpeet 2006

Wk	Date	Reading (C=Carroll)	Lecture notes / topic
1	w14sep	[none]	Introduction to the course and the prof.
	f16sep	my OSC lecture	Review of Lorentz transformations, rapidity; x^μ and the Minkowski metric η_μν
2	w21sep	[C online pp1-12]	Invariant interval, causality; vectors
	f23sep	[C online pp8-19]	Tensors; vectors and dual vectors; Coordinate bases; Kronecker δ^μ_ν
3	w28sep	[C online pp14-21 and OSC lecture pp12-14]	Manipulating tensors; 4-momentum p^μ ; Levi-Civita ε_μναβ , EM field F_μν; Constant acceleration & Twin Paradox
	f30sep	Carroll book sec. 3.1	Equivalence principle; gravity as geometry; Tensors in curved space
4	w05oct	3.2-3.3	Parallel transport and covariant derivative ∇_μ ; Christoffel connection Γ^μ_νλ
	f07oct	3.3-3.4	Parallel transport and the geodesic equation; affine parameter; an explicit example
5	w12oct	2.3, 3.8 & Appendix B	Vector field commutators and Lie derivatives; role of symmetries and Killing vectors; examples
	f14oct*	Appendix J	Orthormal frames and non-coordinate bases e^A; spin connection one-form ω^A_B
6	w19oct	3.6-3.7	Riemann two-form R^A_B , Riemann curvature R^λ_σμν
	f21oct	3.9	Geodesic deviation; Riemann curvature example from 2004 exam
7	w26oct	3.10	Ricci tensor R_μν and scalar R ; how symmetries reduce complexity
	f28oct	1.9-1.10,3.5	Energy-momentum tensor T_μν , e.g. perfect fluid; covariant conservation
8	w02nov	4.1,4.2	Newtonian limit; Why a tensor theory of gravity?
	f04nov*	4.3	Action for gravity and obtaining Einstein's equations
9	w09nov	4.4	Einstein field equations
	f11nov	4.4,4.5	Finding energy-momentum tensor in general; e.g.s spin-0 & spin-1 fields, cosmological constant, particle
10	w16nov	4.6, Appendix F	Bending of geodesics by gravity: Raychaudhuri equation; energy conditions
	f18nov	5.1,5.2,5.8	Birkhoffs's theorem; hydrostatic equilibrium and Tolman-Oppenheimer-Volkoff (TOV) equations
11	w23nov	5.1-5.3,5.8	Schwarzschild black hole solution; Event Horizon and Singularity; matching to TOV
	f25nov	5.4-5.5	Singularities and Geodesics in Schwarzschild
12	w30nov	5.6-5.7, Appendix G	Precession of perihelion of Mercury; Causal structure of Schwarzschild
	f02dec*	6	Causal structure of black holes; Surface gravity; charged/rotating black holes
13	w07dec	[none]	Hawking radiation, black hole entropy, extra dimensions and string theory
	f09dec	all lecture notes & HW solutions	Solving exam-type problems

* = homework assignment due by 1:10pm

Advice

To view PDF files, you should have Adobe Reader [offsite link].

Here is a table of the Greek alphabet for your reference.

Please make sure you read the assigned sections of Carroll (the course textbook) before turning up to each class. Doing the assigned reading will make each lecture more comprehensible and much more valuable for you. Assigned reading will be posted no less than two days before a lecture.

I number important equations in my lecture notes, to help you synchronize with auxiliary notes you may take during class.

Digitised lecture notes will be uplinked soon after each lecture. Since important in-lecture annotations to prepared notes will be made, uplinking of course lecture notes prior to lecture would be inconsistent with causality and hence will not be done. I also have other sound educational reasons for loading lecture notes after the fact - not to mention the common phenomenon of last-minute titivations. Please also remember that I am providing lecture notes as a service, primarily to be welcoming to students with disabilities. So please don't argue with me about my post-lecture uploading policy... Thanks.

Important deadlines and dates can be found on the Arts and Science Calendar Sessional Dates page .

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Canada License.