Math. 489GR
9 April 2008
(Fulling)
Test B Solutions to nonessay questions
1. (40 pts.) Consider the two-dimensional space-time with metric
ds2 = dt2 + t2 dx2
( < x < ,
0 < t < ) .
Note that parts (a) and (b) can be done in either order.
(a) Find the diere
Math. 489GR
November 2009
Test B Solutions
1. (35 pts.) A two-dimensional space-time has the metric tensor given by the line element
ds2 = dt2 + cosh2 t dx2
(i.e., gtt = 1, gxx = cosh2 t, gxt = 0).
(a) Find the geodesic equation (the equation of motion of
Math. 489GR
20 February 2008
(Fulling)
Test A Solutions
Extra Credit: The test is worth 120 points, but 100 counts as a perfect score.
1. (30 pts.)
(a) Sam is moving in the positive x direction at speed v relative to me. Write down the
Lorentz transformat
Math. 460
12 October 2011
(Fulling)
Test A Solutions
1. (30 pts.) Start with a (contravariant) vector space V .
(a) Dene a 0 tensor in the modern fashion (as a multilinear functional . . . ).
3
A 0 tensor is a multilinear functional of three vector argume
Math. 489GR
5 May 2008
(Fulling)
Open-Book Final Examination Solutions
1. (70 pts.) A two-dimensional space-time is called conformally at if there exist coordinates
in which the line element (metric) takes the form ds2 = C (t, x)(dt2 + dx2 ) . We shall
as
Math. 489GR
15 Dec 2009
(Fulling)
Final Examination Solutions
1. (Multiple choice each 5 pts.)
(a) What is the curvature scalar of the metric ds2 = dt2 + x2 dx2 ?
(A) A positive constant, because this is one of the many known forms of the de Sitter
metric
Math. 460
9 December 2011
(Fulling)
Final Examination Solutions
1. (40 pts.) In 4-dimensional space-time the Riemann tensor, R , has 44 = 256 components. Show why only 20 of them are independent. (Start by listing the index symmetries.)
The tensor is anti