2002/01/30 by Christoph Schmid, Schmid, Christoph
Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #astro-ph #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0201095
10 pages, to appear in Proc. COSMO-01, Rovaniemi, Finland, Aug 29 - Sep 4, 2001
arxiv created 2002/01/30 · arxiv updated 2009/11/30
The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed, spatially flat FRW cosmology, we consider cosmological vorticity perturbations (i.e. vector perturbations, rotational perturbations) at the linear level. We ask: Will cosmological rotational perturbations drag the axis of a gyroscope relative to the directions (geodesics) to galaxies beyond the rotational perturbation? We cast the laws of Gravitomagnetism into a form showing clearly the close correspondence with the laws of ordinary magnetism. Our results are: 1) The dragging of a gyroscope axis by rotational perturbations beyond the H radius (H = Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the H radius, then the dragging of the gyroscope axis by the rotational perturbation is exact for any equation of state for cosmological matter. 3) The time-evolution of a gyroscope axis exactly follows a specific average of the matter inside the H radius for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity.