Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-07-19
Class. Quantum Grav. 25 (2008) 165018
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scheduled to appear in Class. and Quantum Grav. July 2008, "inertial" added in title
Scientific paper
10.1088/0264-9381/25/16/165018
We calculate the rotation of the inertial frames within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has only one Killing vector. It is along the z-axis and hypersurface orthogonal. We solve the Einstein equations to first order in the wave amplitude and superpose such linearized solutions to form a wave pulse. We then solve the relevant Einstein equation to second order in the amplitude to find the rotation of inertial frames produced by the pulse. The rotation is without time delay. The influence of gravitational wave angular momentum on the inertial frame demonstrates that Mach's principle can not be expressed in terms of the influence of the stress-energy-momentum tensor alone but must involve also influences of gravitational wave energy and angular momentum.
Bicak Jiri
Katz Joseph
Lynden-Bell Donald
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