Search

The SEE (Satellite Energy Exchange) mission was suggested and designed under NASA Project in 1992–2002 to make extremely accurate measurements on fundamental gravitation by observing the orbital perturbation of unconstrained orbiting test bodies in a femto-g to atto-g environment. The mission uses novel and original test body dynamics. Its broad objective is to support the development of gravity theory and its unification with other interactions by carrying out sensitive gravitational tests capable of discriminating among alternative theories. The SEE mission introduced and utilized new technology for near-zero-g environment creation, passive cryogenic temperature control, passive station-keeping capability, and non-contact sub-micron-accuracy distance measurements, all of which promise to have a wide variety of applications.

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, an electromagnetic composite brane ansatz is adopted, and certain restrictions on the branes are imposed, the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases.

This paper is a brief review of integrable models of gravitation and cosmology in four and more dimensions which make up one of the proper approaches to studying the basic issues and strong field objects, the early and present Universe, and black hole (BH) physics in particular. The main results within this approach, obtained in the recent years by the research group founded by K.P. Staniukovich, are presented. Absolute G measurements and problems of its possible time and range variations, which are reflections of the unification problem, are discussed within these models. The choice, nature, classification and precision of determination of fundamental physical constants and their role in the expected transition to new definitions of basic SI units, supposed to be based on fundamental physical constants and stable quantum phenomena, are described. A need for further absolute measurements of G, its possible range and time variations is stressed. Themultipurpose space project SEE is shortly described, aimed at measuring G and its stability in space and time with a progress of 2–3 orders of magnitude against the present accuracy. It may answer many important questions posed by gravitation, cosmology and unified theories. A project of a laboratory experiment to test possible deviations from Newton’s law of gravity is also presented.

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions $\mathcal{H}_s $ (for fluxbranes) and H s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for $\mathcal{H}_s $ and H s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H s and $\mathcal{H}_s $ , as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials $\mathcal{H}_s $ were shown to be used for the construction of black brane polynomials H s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A 2, C 2, and G 2.

Bianchi type I cosmological model in (n+1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quantum billiard for an 11D model with 120 4-forms which mimics SM2-brane sector of D=11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved., Comment: 14 pages, LaTex, no figures, several typos are eliminated

We review spherically symmetric solutions with a horizon in two models: (i) with scalar fields and fields of forms, and (ii) with a multi-component anisotropic fluid. The metrics of the solutions are defined on a manifold that contains a product of n − 1 Ricci-flat “internal” spaces. The solutions are governed by functions H s obeying nonlinear differential equations with certain boundary conditions. Simulation of black-brane solutions is considered, and the Hawking temperature is calculated. For the fluid solution, the post-Newtonian parameters β and Γ corresponding to the 4-dimensional section of the metric are found.