Semiclassical behavior of uniform-density models for cosmic strings and relativistic stars

In this paper we show how quantum corrections, although perturbatively small, may play an important role in the analysis of the existence of some classical models. This, in fact, appears to be the case of static, uniform-density models of the interior metric of cosmic strings and neutron stars. We consider the fourth-order semiclassical equations and first look for perturbative solutions in the coupling constants alpha and beta of the quadratic curvature terms in the effective gravitational Lagrangian. We find that there is not a consistent solution; neither for strings nor for spherical stars. We then look for nonperturbative solutions and find an explicit approximate metric for the case of straight cosmic strings. We then conclude that nonperturbative solutions are valuable for describing certain physical situations.