Year: 2012
Type: article
Abstract: The bi-tensor kernel in the integral form of Einstein equations realizing Mach's idea of nonexistence of empty space-times is taken as an inverse of the differential operator (''Mach operator'') defined conventionally as a second variation of Einstein's gravity action over contravariant components of the metric tensor. The choice of transverse gauge condition used in this definition does not influence results of the paper since only transverse and traceless tensor modes written on different background space-times are studied. The presence of ghosts among modes of the Mach operator invalidates the integral formulation of Einstein equations. And the demand of the absence of these ghosts proves to be a selection rule for dimensionality of the background space-time. In particular, the Mach operator written on the De Sitter background or on the background of the so-called ``Einstein Universe'' does not possess tensor ghosts only in four dimensions. The similar demand gives a nontrivial formula for dimensionalities of subspaces of the Freund--Rubin background.
Author: Boris L. Altshuler
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2042866462