We discuss scenarios in which the galactic dark matter in spiral galaxies is described by a long range coherent field which settles in a stationary configuration that might account for the features of the galactic rotation curves. The simplest possibility is to consider scalar fields, so we discuss, in particular, two mechanisms that would account for the settlement of the scalar field in a nontrivial configuration in the absence of a direct coupling of the field with ordinary matter: topological defects and spontaneous scalarization.

We study in the physical frame the phenomenon of spontaneous scalarization that occurs in scalar-tensor theories of gravity for compact objects. We discuss the fact that the phenomenon occurs exactly in the regime where the Newtonian analysis indicates it should not. Finally, we discuss the way the phenomenon depends on the equation of state used to describe nuclear matter.

The inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the continuous spontaneous localization model of wave function collapse in the context of inflation. This modification of quantum dynamics introduces a stochastic nonunitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We show, by proper choice of the collapse-generating operator, that it is possible to achieve compatibility with the precise observations of the cosmic microwave background radiation.

The concept of an “isolated horizon” has been recently used to provide a full Hamiltonian treatment of black holes. It has been applied successfully to the cases of nonrotating, nondistorted black holes in the Einstein vacuum, Einstein-Maxwell, and Einstein-Maxwell-dilaton theories. In this paper, the extent to which the framework can be generalized to the case of non-Abelian gauge theories is investigated in which “hairy black holes” are known to exist. It is found that this extension is indeed possible, despite the fact that, in general, there is no “canonical normalization” yielding a preferred horizon mass. In particular the zeroth and first laws are established for all normalizations. Colored static spherically symmetric black hole solutions to the Einstein-Yang-Mills equations are considered from this perspective. A canonical formula for the horizon mass of such black holes is found. This analysis is used to obtain nontrivial relations between the masses of the colored black holes and the regular solitonic solutions in Einstein-Yang-Mills theory. A general testing bed for the instability of hairy black holes in general nonlinear theories is suggested. As an example, the embedded Abelian magnetic solutions are considered. It is shown that, within this framework, the total energy is also positive and thus the solutions are potentially unstable. Finally, it is discussed which elements would be needed to place the isolated horizon framework for Einstein-Yang-Mills theory on the same footing as the previously analyzed cases. Motivated by these considerations and using the fact that the isolated horizon framework seems to be the appropriate language to state uniqueness and completeness conjectures for the EYM equations, in terms of the horizon charges, two such conjectures are put forward.