  The conserved charge called Y-ADM mass density associated with asymptotically
translational Killing-Yano tensor gives us an appropriate physical meaning
about the energy density of $p$ brane spacetimes or black strings. We
investigated the positivity of energy density in black string spacetimes, using
the spinorial technique introduced by Witten. Recently, the positivity of Y-ADM
mass density in p brane spacetimes was discussed. In this paper, we will extend
this discussion to the transversely asymptotically flat black string spacetimes
containing an apparent horizon. We will give the sufficient conditions for the
Y-ADM mass density to become positive in such spacetimes.
