HOMEWORK
MTH 437/537

Links to assignments and solutions are to PDF files, which require a PDF viewer such as Acrobat Reader.
(Other formats may be possible; ask me.) Solutions are password protected; see me for access.
(The summaries of the problems as stated on this page are just that; please download the PDF files.)

• HW 0: Send me email.
  Please send an email message to me at tevian@math.orst.edu. I will use this to make a mailing list to enable me to send information to the entire class. If you don't check your email regularly, please let me know. Please include some information about yourself, such as your math/physics background and your motivation for taking this class.

• HW 1: Special Relativity Paradox. Due Friday, 9 April 1999
  Resolve the pole and barn paradox OR resolve any paradox on the list of other paradoxes.
  "Resolve" means to (correctly!) explain what happens in both reference frames. This can be in words, using a spacetime diagram, via an explicit, numerical computation, or some combination of these.
  Solutions

• HW 2: Tensor Algebra. Due Monday, 19 April 1999
  Show that timelike vectors cannot be orthogonal to null vectors or to other timelike vectors. Show further that 2 null vectors can only be orthogonal if they are parallel. In addition, if u=x-y and v=y, where x,y are the usual coordiantes in the plane, find the coordinate basis vectors, the corresponding dual basis of 1-forms, and the metric (line element) in the u,v coordinate system.
  Solutions

• HW 3: The Sphere. Due date extended to Friday, 30 April 1999
  (Original due date: Wednesday, 28 April 1999.)
  On the sphere of radius r, find the Christoffel symbols, the Riemann tensor, the Ricci tensor, and the Ricci scalar. Furthermore, write down the geodesic equation, verify that the equator is a solution, and argue that the geodesics on the sphere are great circles.
  You may find my notes on algebraic computing in relativity helpful when working the homework problems. Please note the following ground rules:
  
  You may do all tensor computations using any basis you wish; the 2 standard choices are a coordinate basis, in which case you should probably use the formulas for the components of these tensors, and an orthonormal basis, in which case you may prefer to work with differential forms.
  You may use algebraic software to check your answer, but then please include a printout of your session. You still must show me your full calculation by hand.
  Solutions

  HW 4: Global structure. Due Friday, 28 May 1999
  Show that the line element ds² = -dT² - 2 sinh(X) dT dX + dX² + dY² + dZ² is just the Minkowski line element ds² = -dt² + dx² + dy² + dz² in funny coordinates.
  Some hints are given in the PDF file.
  Solutions