English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We show that the dragging of the axis directions of local inertial frames bya weighted average of the energy currents in the universe is exact for alllinear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K =(+1, -1, 0) and of Einstein's static closed universe. This includes FRWuniverses which are arbitrarily close to the Milne Universe, which is empty,and to the de Sitter universe. Hence the postulate formulated by E. Mach aboutthe physical cause for the time-evolution of the axis directions of inertialframes is shown to hold in cosmological General Relativity for linearperturbations. The time-evolution of axis directions of local inertial frames(relative to given local fiducial axes) is given experimentally by theprecession angular velocity of gyroscopes, which in turn is given by theoperational definition of the gravitomagnetic field. The gravitomagnetic fieldis caused by cosmological energy currents via the momentum constraint. Thisequation for cosmological gravitomagnetism is analogous to Ampere's law, but itholds also for time-dependent situtations. In the solution for an open universethe 1/r^2-force of Ampere is replaced by a Yukawa force which is of identicalform for FRW backgrounds with $K = (-1, 0).$ The scale of the exponentialcutoff is the H-dot radius, where H is the Hubble rate, and dot is thederivative with respect to cosmic time. Analogous results hold for energycurrents in a closed FRW universe, K = +1, and in Einstein's closed staticuniverse.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with $K = (\pm 1, 0)$