Cosmological vorticity perturbations, gravitomagnetism, and Mach's principle
Jan, 2002Citations per year
Abstract: (arXiv)
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 radius (H = Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the 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 radius for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity.References(6)
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