  The static stationary axially symmetric background ("infinite cosmic string")
of the $D=4$ string theory provided with an axion charge is studied in the
effective theory approach. The most general exact solution is constructed. It
is found that the Kalb-Ramond axion charge, present in the string topology
$R^{3} \times S^{1}$, produces nontrivial gravitational field configurations
which feature horizons. The corresponding ``no-hair'' theorems are proved which
stress uniqueness of black strings. Connection of the solutions with the gauged
WZWN sigma model constructions on the world sheet is discussed since they are
the only target spaces which hide their singularities behind horizons, and thus
obey the cosmic censorship conjecture.
