Gravitational collapse of a macroscopic string by a Newtonian description including the effect of gravitational radiation

Abstract

We make an attempt to dynamically study, in four space-time dimensions, the classical gravitational collapse of a macroscopic circular fundamental string, by a truncation of the Einstein equations that suppresses retarded features but keeps the main self-gravity peculiarities of the relativistic string dynamics, and allows the investigation of a possible infinite red-shift. The numerical solution of the string evolution in the self-induced metric shows an infinite red shift at a macroscopic size of the string, when the string reaches the velocity of light. We further include the back-reaction of the radiation of gravitons which induces energy dissipation: now the velocity of light is not reached, the infinite red-shift does not form and the string simply shrinks with damped oscillations.