Aspects of the gravitational and thermal physics of solitons in field theory

We numerically study classical soliton solutions to two physically relevant field theories in an astrophysical setting, and through the Euclidean path integral formalism of finite-temperature field theory, we develop a new analytical method to study solitons semiclassically in a cosmological setting. By carefully considering non-Abelian gauge theories coupled to classical Einstein gravity, we demonstrate how black hole solutions to such theories can have nontrivial field structure outside the event horizon, despite the widely held belief to the contrary known as the "no-hair" conjecture. We next obtain numerical particle-like soliton and black hole solutions in the spontaneously broken phase of the Einstein-Yang-Mills-Higgs system, which consists of an SU(2) gauge field coupled to a Higgs doublet (the electroweak standard model without hypercharge). We also obtain such solutions to the related Einstein-Non-Abelian-Proca theory as a prelude to the gauge field case. Using the bosonic part of the low-energy heterotic string action, we then construct string-inspired regular and black hole solutions to Einstein-Yang-Mills theory coupled to massive dilaton and axion fields. Though we present numerical solutions only for the case of a trivial axion field, we analyze the full system and discuss the feasibility of additional solutions. Shifting from classical to quantum field theory, we next develop a general method utilizing collective coordinates and Euclidean functional constraints to study solitons semiclassically in the path integral formulation of Euclidean quantum field theory. Our method is an extension of the existing semiclassical method, which does not accomodate Euclidean time or the usual canonical Euclidean formalism, and applies to both time-independent solitons and solitons with time-dependence arising from global charge symmetries. We illustrate the method through an example finite-temperature field theory calculation: the one-loop partition function for time-dependent, nontopological soliton solutions to a complex scalar theory in (3 + 1)-dimensions.