  Differential properties of a spin 2 boson field $\psi_{\mu\nu}$ describing
propagation of gravitational perturbations on a straight cosmic string's
space-time background are studied by means of methods of the differential
spaces theory. It is shown that this field is a smooth one in the interior of
cosmic string's space-time and looses this property at the singular boundary
except for cosmic string space-times with the following deficits of angle:
$\Delta=2\pi (1-1/n) $, $n=1,2,...$. A relationship between smoothness of
$\psi_{\mu\nu}$ at the singularity and the gravitational conical bremsstrahlung
effect is discussed. A physical interpretation of the smoothness notion is
given. It is also argued that the assumption of smoothness of $\psi_{\mu\nu}$
at the singularity plays an equivalent role to the Aliev and Gal'tsov
"quantization" condition.
