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Unformatted text preview: Physics 523 Final Exam, Fall 2010 Wednesday, January 12, 1:30-4:30pm This exam consists of 4 problems (with multiple parts) on 2 pages, with a total of 100 pts. Do all problems, answered in the exam booklet provided, and clearly show all your work. This is a closed-book exam. Non-programmable calculators may be used (though should not be necessary). Remember to write your name in the exam booklet, and write and sign the pledge : I pledge my honor that I have not violated the Honor Code during this examination. Problem 1. [30 pts total] To linear order, in TT gauge, the metric for a plus-polarized gravitational wave, traveling in the z direction, with constant amplitude A and frequency ω , is described by the following metric: ds 2 = − dt 2 + [1 + A cos( ω ( t − z ))] dx 2 + [1 − A cos( ω ( t − z ))] dy 2 + dz 2 (a) [10 pts] Show that a time-like observer at a constant spatial coordinate location ( t,x,y,z ) = ( t,x ,y ,z ) is a geodesic of the above metric. (b) [20 pts] An observer at the origin ( x,y,z ) = (0 , , 0) emits two photons at the same time t = 0, one that travels in the + x direction, the other in the +...
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This note was uploaded on 02/02/2012 for the course PHY 523 at Princeton.