Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-10-19
Acta Phys.Polon.B39:1849-1868,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages; v3: somewhat extended; v4: accepted for publication in Acta Physica Polonica B
Scientific paper
The gravitational field exterior respectively interior to a metrically stationary, axially symmetric, isolated spinning source made of perfect fluid is examined within the quasi-metric framework. (A metrically stationary system is defined as a system which is stationary except for the direct effects of the global cosmic expansion on the space-time geometry.) Field equations are set up and solved approximately for the exterior part. To lowest order in small quantities, the gravitomagnetic part of the found metric family corresponds with the Kerr metric in the metric approximation. On the other hand, the gravitoelectric part of the found metric family includes a tidal term describing the effect of source deformation due to the rotation. This tidal term has a counterpart in Newtonian gravitation, but not in the Kerr metric. Finally, the predicted geodetic effect for a gyroscope in a circular orbit is calculated. There is a correction term, unfortunately barely too small to be detectable by Gravity Probe B, to the standard expression.
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