Centenary of Einstein’s general relativity. Its present extensions

Abstract

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. The multipurpose 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.

On Cosmology in Nonlinear Multidimensional Gravity with Multiple Factor Spaces

“…where the metric g ab is used, the indices are raised and lowered with g ab and g ab , and V E(Cas) is the Casimir contribution to the total Einstein-frame potential obtained from V J(Cas) after the transformation (9). The quantities β i and σ are expressed in terms of the n fields φ i , whose numbers coincide with the numbers of factor spaces.…”

Wormholes and black universes communicated with extra dimensions

“…It describes a spherically symmetric, twice asymptotically flat wormhole in the 4D subspace M 0 × M 1 with a toroidal extra space M 2 having a unit size, p − at u = 0 (that is, z = −∞) and the size p + = e nπ/k p − at the other end, u = π/k, corresponding to z = +∞. 2 Suppose that the size of extra dimensions p − on the left end, z = −∞, is small enough to be invisible by modern instruments, say, p − = 10 −17 cm. The size p + on the other end is much larger if n/k is large enough.…”

“…Multidimensional theories suggest a great variety of geometries, topologies and compactification schemes (for reviews see, e.g., [1][2][3][4] and references therein). One of the opportunities of interest is that the geometry can be effectively four-dimensional in some space-time region but have a greater dimension in other regions.…”

Cosmology in nonlinear multidimensional gravity and the Casimir effect

“…The idea of extra dimensions is now firmly established in theoretical physics in many contexts, such as Kaluza-Klein theories, supergravity, strings and M-theory, brane-world theories. This idea provides a powerful methodological framework for many crucial problems: geometric unification of physical interactions, the hierarchy problem, possible variations of fundamental constants as well as searches for realistic cosmological scenarios including inflationary, string or brane backgrounds, see, e.g., [1,2] and references therein.…”