As noted in the main class website I intend to follow the order of topics in the text by Thomas Moore, A General Relativity
Workbook.
I will append handouts of my own design in an order that seems useful to me; they will become available from the class website.
More detailed information will appear here before the end of the summer (of 2018).
Although not technically a part of the Syllabus, this is perhaps a useful place to note that for any room that contains 10 different scientific researchers in general relativity, there will generally be at least 12 to 13 different sign conventions used by the persons in that room. Therefore, when consulting literature on topics in this class---which it is very important for you to do regularly and often---one must always compare sign conventions. For example, you will note that Moore's textbook mentions some of his important sign conventions at the bottom of the inside front cover of the book.
Finley uses (+1,+1,+1,-1) for the diagonal entries in the standard form of the (Minkowski) metric, as explained more in the notes on conventions,
which is, unfortunately, slightly different from Moore's choice of (-1,+1,+1,+1), the entries being the same, but the order being different; both these orders are quite common, Finley's approach coming from an ordering of the coordinates as (x,y,z,t), while Moore's ordering comes from expressing the (same) coordinates in the order (t,x,y,z). Do NOTE that this difference in order of coordinates can cause matrices---where one generally does not bother to indicate the ordering of coordinates---to appear very different!
Please watch and do not get confused by these different conventions!
As well Finley chooses values for units so that c, and (usually G), are equal to 1. Moore uses the same sorts of units, which he refers to as GR units. Again he has a nice conversion chart between SI units and GR units on the inside front cover of his text.
The more detailed syllabus will be ready by the end of the summer!
| Beginning date & no. of weeks |
General Topic | Some Details |
| 20 August | Einstein's Equivalence Principle(s) |
General Introductory Discussion; Ideas of Spacetime Principle of Equivalence, via the experiments of Eötvös, Dicke, Braginsky, etc. and then those of Pound and Rebka, on the red-shift when accelerating |
| 27 August 1 week |
4-dimensional Spacetime and Special Relativity; Using tangent vectors to understand tangent (vector) spaces and their dual spaces (1-forms); |
events, 4-vectors, Minkowski diagrams, an observer's future and past, light cones;
difficulties with simultaneity ; worldlines; the Minkowski interval as metric; Lorentz transformations (first look); Vectors, (3+1 divisions of 4-vectors), 1-forms, Direct products, tensors, Wedge products Tensors as Multi-linear Operators on Vectors and 1-forms ; Tensor Transformation Laws; 4-momentum, 4-force and 4-acceleration; Manifolds, tangent and co-tangent spaces, using d(location)/dλ to describe a curve; |
| These were examples | ||
Last updated/modified: 10 May, 2018
Comments and Questions to Daniel Finley---
finley@unm.edu