Cosmological vorticity perturbations, gravitomagnetism and Mach's principle

by C. SCHMID (ETH, Zurich)

Thursday 16 Nov 2000, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed FRW cosmology, we consider cosmological vorticity perturbations (i.e. rotational perturbations, vector perturbations). We ask: Will the cosmological rotational perturbations drag the axis of a gyroscope relative to the directions 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 horizon is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the horizon, then the dragging of the gyroscope axis by the rotational perturbation is exact. 3) The time-evolution of the gyroscope axis exactly follows the average of the matter inside the horizon for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity.