Gravitational Conical Bremsstrahlung and Differential Structures

TL;DR

This paper investigates the differential properties of gravitational perturbations around cosmic strings, revealing conditions under which these fields are smooth and linking this to gravitational bremsstrahlung effects.

Contribution

It introduces a novel analysis of gravitational perturbations on cosmic string backgrounds using differential spaces theory, connecting smoothness at singularities to physical phenomena.

Findings

Smoothness of gravitational fields depends on the deficit angle of the cosmic string.

Smoothness at the singularity relates to gravitational conical bremsstrahlung.

The smoothness condition is analogous to a quantization condition in the theory.

Abstract

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.