Centenary of Einstein’s general relativity. Its present extensions

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.