  We investigate stationary string solutions with spacelike worldsheet in a
five-dimensional AdS black hole background, and find that there are many
branches of such solutions. Using a non-perturbative definition of the jet
quenching parameter proposed by Liu et. al., hep-ph/0605178, we take the
lightlike limit of these solutions to evaluate the jet quenching parameter in
an N=4 super Yang-Mills thermal bath. We show that this proposed definition
gives zero jet quenching parameter, independent of how the lightlike limit is
taken. In particular, the minimum-action solution giving the dominant
contribution to the Wilson loop has a leading behavior that is linear, rather
than quadratic, in the quark separation.
