Inertial frame rotation induced by rotating gravitational waves

Abstract

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.

Scheduled to appear in Class. and Quantum Grav. July 2008, "inertial" added in title

References in corpus (5)

• Asymptotic Structure of Symmetry Reduced General Relativity
• Gravitational radiation from Schwarzschild black holes: the second order perturbation formalism
• The Double Pulsar System J0737-3039: Modulation of A by B at eclipse
• Cosmological perturbation theory, instantaneous gauges and local inertial frames
• Gravitational waves and dragging effects

Cited by in corpus (9)

• Cosmological equivalence principle and the weak-field limit
• Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with $K=(\pm 1,0)$
• Gravitational waves and dragging effects
• Effects of rotating gravitational waves
• Construction and application of variations on the cylindrical gravitational waves of Weber, Wheeler, and Bonnor
• Rotation of inertial frames by angular momentum of matter and waves
• Effects of the circularly polarized beam of linearized gravitational waves
• Charged cosmic strings interacting with gravitational and electromagnetic waves
• Dragging of inertial frames by matter and waves