  We consider the gravitational field of infinite straight and stationary
twisted Baby Skyrmion cosmic string. Using the approximate solution of Einstein
equations, it is shown that the internal phase rotation (twist) along the
string axis is responsible for a long-range gravitational acceleration
resembling that of massive cylindrical shell. We also study the stability and
gravitational field of circular loops. When the loop radius becomes comparable
with the string width, the rigidity energy tends to stabilize small loops
against radial collapse. The nucleon scale-toroidal knot with Hopf charge Q=1
is found to decay very rapidly on the scale of the age of the universe due to
low energy cost to flux lines crossings. Such knot is therefore excluded from
the dark matter scenario of Spergel and Steinhardt. However, the Q = 0 loop,
stabilized by rigidity, could be a candidate for this scenario. In contrast,
the electroweak strings are prevented from intercommuting due to much larger
energy cost to intersection. This makes them a possible candidate for the solid
dark matter scenario of Bucher and Spergel.
