Possible ways of formalizing the concept of statistically homogeneous and isotropic curvature fluctuations in general relativity are considered. The straightforward way of constructing this concept, which is borrowed from statistical hydromechanics, is shown to lead to a physically degenerate result: the correlations between the fluctuations do not decrease with increasing distance between the points. It is emphasized that this result is a peculiar analogue of the Schur theorem.
Department of Mathematics, Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Science News of the Faculty of Physics, Lomonosov Moscow State University
This new information publication, which is intended to convey to the staff, students and graduate students, faculty colleagues and partners of the main achievements of scientists and scientific information on the events in the life of university physicists.