The response functions of a detector at rest in the gravitational field of a cosmic string as well as a detector moving uniformly nearby the string are calculated and different asymptotic regimes are analysed.
1. Cosmic string metrics
One of the currently studied problems is the investigation of quantum processes in curved space-times. The permanent interest in this problem during the last ten years comes not only from the existence of remarkable physical effects produced by gravitational fields but also from the development of quantum gravity theory. In this respect these investigations remind one of the initial epoch of quantum field theory when the electromagnetic field was considered as an external classical field interacting with quantized matter. However, external gravitational fields cause much more problems, both calculational and fundamental ones.
That is the reason why the choice of a suitable gravitational field for this type of investigations seems to be very important. First of all it is necessary to avoid supertluous hard calculations and to bypass possible fundamental problems. Secondly, the gravitational field must be nontrivial to take into account essential features of the processes under study.
The gravitational field of a straightline cosmic string can be considered as very suitable for this aim. The space-time around the string is locally flat. It allows to use conventional methods of quantum field theory. At the same time the gravitational field of the cosmic string possesses characteristics which are typical for general relativity.
The aim of the present paper is to investigate how the gravitational field of the cosmic string influences quantum fluctuations of a massless scalar quantum field by means of studying of the behavior of a detector moving or placed nearby the cosmic string.
Strings as extended objects appeared firstly in the paper by Nielsen and Olesen [ 11, who showed that Higgs's Lagrangian allows string solutions by an analogy with second type superconductors.
Later, Zel'dovich et al.
[2] found that strings as well as domain walls and monopoles can arise in the form of topological defects in the early Universe. It can happen due to its expansion and cooling below a critical temperature when the Higgs field acquires its nonzero vacuum value (see reviews [ 3,4] ).