  The purpose of this paper is to illustrate the problem of energy and momentum
distributions of Van Stockum space-time within the framework of two different
theories of gravity, general relativity and teleparallel gravity.
  We have shown that for all homogeneous space-times with metric components
$g_{\mu\nu}$ being functions of time variable, $t$, alone and independent of
space variables the total gravitational energy for any finite volume is
identically zero. By working with general relativity, we have calculated the
energy-momentum density for Van Stockum space-time using double index complexes
and in the framework teleparallel gravity, we used the energy-momentum
complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. In our analysis,
we sustained that general relativity and teleparallel gravity are equivalent
theories of space-time under consideration. For space-time under consideration,
we have shown that different complexes of energy-momentum density do not
provide the same results neither in general relativity nor in teleparallel
gravity.
