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Phys 503 / 729: General Relativity and Gravitation
Fall 2015 – Assignments and Other Announcements

 12.04: Final Exam: As discussed in class, the final exam will be on Monday, December 7th, from 1:00 to 4:00 pm (we have moved it back by 1 hour with respect to the original schedule). We will meet in our usual lecture room; a possible room change will be announced at that time. Topic checklist, html and pdf versions.   12.02: Homework Assignment #7: Phys 503: Derive Eq. 7.32; Problems 7.7, 8.5. Phys 729: Problems 7.7, 8.1, 8.5. Optional; If you submit it, turn it in by Wednesday, Dec 9.   11.02: Homework Assignment #6: Three problems that can be found here. Due Monday, Nov 9.   10.21: Homework Assignment #5: Three problems that can be found here. Due Wednesday, Oct 28.   10.05: Homework Assignment #4: Three problems due Monday, Oct 12 [notice new date]: Carroll, Ch. 3, Exercises 4, 7, 8. [There is now a Mathematica notebook available, with solutions to 2 of the 3 problems.]   09.24: Makeup Class and Review / Problem Sessions: Based on the results of the Doodle poll, starting next week (September 30th), we will be meeting on Wednesdays from 1:00 to 1:50 in addition to the regular 11:00-11:50 class. The first meeting will be a makeup class (the last one, hopefully); after that at these meetings we will review and discuss questions and problems.   09.23: Homework Assignment #3: Three problems due Monday, Sep 28: Carroll, Ch. 2, Exercises 5, 6, 7.   09.23: Quiz #2: Quiz #2 will be given on Friday, September 25, at the beginning of the class period. Checklist of things to know: (i) Be able to manipulate tensors similarly to Exercise 1.7 (from homework #2), and (ii) use transformation laws for tensors like in Exercise 1.10 (from homework #2) (iii) Know what the following are: manifold, metric, vector, dual vector, Riemannian and Lorentzian metric, tensor. (iv) Be familiar with expressions for a metric in matrix form and in line element form, and be able to use the metric to lower or raise indices, find the inverse metric, calculate scalar products. (v) Know what a FLRW ("Robertson-Walker") metric is and what it representes physically. (vi) Know what the following are: causal/chronological future and past, domain of dependence, Cauchy surface, globally hyperbolic spacetime.   09.16: Homework Assignment #2: Three problems due Monday, Sep 21: (1) Carroll, Ch. 1, #7; (2) Carroll, Ch. 1, #10; (3) Carroll, Ch. 2, #4.   09.11: Quiz #1: Quiz #1 will be given on Monday, September 14, at the beginning of the class period. The material will be what is covered in lecture notes L01 and L02, including Sections 1-4 of Carroll's book.   09.09: Homework Assignment #1: Three problems due Monday, Sep 14: (1) Carroll, Ch. 1, #5; (2) Carroll, Ch. 1, #6; (3) A 5-m long car moving at a relativistic speed, i.e., a considerable fraction of the speed of light, is headed straight for the front door of a garage that has the same 5-m length (in both cases what is given is the proper length). The front door of the garage is open, while the back door is closed. The car does not slow down as it enters the garage, but the garage is equipped with an automatic mechanism which opens the back door at the exact instant the back of the car crosses the front door. According to pre-relativistic physics the car is barely able to fit into the garage, as the back door is opened precisely when the car is about to crash into it. In special relativity we can take two points of view. (a) According to an observer at rest with respect to the garage, because of length contraction the moving car is shorter than the garage and can fit in it; the car goes through without crashing. (b) In the reference frame of the car driver, because of length contraction the garage is shorter than the car and the car cannot fit into it; the car crashes through the back of the garage before its tail has crossed the front of the garage. Who is right–what actually happens? To answer this problem, you must draw a clear spacetime diagram of the situation, showing the car, the garage and the two reference frames; and you must explain in words your answer to the question. You may show equations, but you may not use any numbers in those equations (you may not use the value of the car and garage rest lengths, which were given for purely illustrative purposes).   09.03: Class Rescheduling: I will be away the whole week of September 7th. This means that we will miss two lectures, those of September 9th and 11th, and we will have makeups for those after I come back. Quiz 1 will be on Monday, September 14th.   08.31: Class Rescheduling: I will be away on Friday, August 28th. As discussed in class, we will make up the missed lecture on Wednesday, September 2nd (we will meet from 11:00 to 11:50 as regularly scheduled, and from 1:00 to 1:50 pm.   08.22: First Class: The class will meet in Lewis 228, on MWF at 11:00–11:50 am; Our first meeting will be on Monday, August 24th.

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