Cosmological Vorticity Perturbations, Gravitomagnetism, and Mach's Principle
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) a...
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| Format: | Report |
| Language: | unknown |
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arXiv
2002
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| Online Access: | https://dx.doi.org/10.48550/arxiv.gr-qc/0201095 https://arxiv.org/abs/gr-qc/0201095 |
| Summary: | 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 $\dot{H}$ radius (H = Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the $\dot{H}$ 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 $\dot{H}$ radius for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity. : 10 pages, to appear in Proc. COSMO-01, Rovaniemi, Finland, Aug 29 - Sep 4, 2001 |
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