  For the five-dimensional spacetimes whose four-dimensional sections are
static, spherically symmetric ($SO(3)$) and flat asymptotically, we study the
behavior of Arnowitt-Deser-Misner mass, tension and momentum densities
characterizing such asymptotically hypercylindrical metrics under boosts along
the cylindrical axis. For such stringlike metrics two boost-invariant
quantities are found, which are a sort of "string rest mass-squared" and the
sum of mass and tension densities. Analogous to the case of a moving point
particle, we show that the asymptotically hypercylindrical geometries can be
classified into three types depending on the value of the "string rest
mass-squared", namely, "ordinary string", "null string" and "tachyonlike
string" geometries. This asymptotic analysis shows that the extraordinary
metrics reported recently by some of the authors belong to the tachyonlike
string. Consequently, it is likely that such extraordinary solutions are the
final states of tachyonic matter collapse. We also report two new vacuum
solutions which belong to the null string and the tachyonlike string,
respectively.
