Vortex Vs Spinning String: Iordanskii Force and Gravitational Aharonov-bohm Effect

We discuss the transverse force acting on the spinning cosmic string, moving in the background matter. It comes from the gravita-tional Aharonov-Bohm effect and corresponds to the Iordanskii force acting on the vortex in superfluids, when the vortex moves with respect to the normal component of the liquid 0.1 Introduction. In superfluids, with their two-fluid hydrodynamics (for superfluid and normal components of the liquid) there are 3 different topological contributions to the force acting on the quantized vortex [1]. The more familiar Magnus force arises when the vortex moves with respect to the superfluid vacuum. For the relativistic cosmic string such force is absent since the corresponding superfluid density of the quantum physical vacuum is zero. However the analog of this force appears if the cosmic string moves in the uniform background charge density [2, 3]. The other two forces of topological origin also have analogs for the cosmic strings: one of them comes from the analog of 1