Dynamics of cosmic string formation with emission of gravitational waves: a toy model

Abstract Starting from an extended theory of general relativity with boundary terms included, we study a toy model to describe the dynamical collapse of an infinite cylinder with positive spatial curvature from which a cosmic string is formed after collapsing, and we examine the production of gravitational waves (GW) emitted during the collapse. The background dynamics of the radial collapse is described by a massive scalar field which departs from the equilibrium when the scalar field climbs through the quadratic potential. During the collapse the radial pressure is considered as null, so that the kinetic and the potential energy densities are equaled. The components of the GW modes $+$, $\times$ and $B$, for the polarization tensor, are analytically obtained.