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There is now an enormously rich variety of experimental techniques being brought to bear on experimental searches for dark matter, covering a wide range of suggested forms for it. The existence of "dark matter", in some form or other, is inferred from a number of relatively simple observations and the problem has been known for over half a century. To explain "dark matter" is one of the foremost challenges today  the answer will be of fundamental importance to cosmologists, astrophysicists, particle physicists, and general relativists.

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the EinsteinVlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian selfgravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the EinsteinVlasov system.

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the EinsteinVlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian selfgravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the EinsteinVlasov system.

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.

Deflection of light by gravity was predicted by General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically. Among them were: the possibility of multiple or ringlike images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility of determining Hubble's constant with lensing.

A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form  dark matter  or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both.

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and sphericallysymmetric models.

The fast progress in improving the sensitivity of the gravitationalwave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometerlong interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity.

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particlelike solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars.

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the EinsteinVlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian selfgravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the EinsteinVlasov system.
