Gravitational Conical Bremsstrahlung and Differential Structures

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.