2004/09/06 by Christoph Schmid, Schmid, Christoph
Earth and Planetary Sciences · Physics and Astronomy · #Astrophysics (astro-ph) #Cosmology and Gravitation Theories #Earth Systems and Cosmic Evolution #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #astro-ph #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0409026
8 pages
arxiv created 2004/09/06 · openalex publication_date 2004/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The axes of gyroscopes experimentally define local non-rotating frames, i.e. the time-evolution of axes of inertial frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed FRW cosmology with k=0 we consider linear cosmological vorticity perturbations and ask: Will cosmological vorticity perturbations exactly drag the axes of gyroscopes relative to the directions of geodesics to galaxies in the asymptotic FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state, are: 1) The dragging of a gyroscope axis by rotational perturbations beyond the H-dot radius (H=Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a perturbation radius, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast, as the perturbation radius gets larger than the H-dot radius. 3) The time-evolution of a gyroscope axis exactly follows a specific average of the matter inside the H-dot radius. In this sense Mach's Principle is a consequence of cosmology with Einstein gravity.