Inertial frame rotation induced by rotating gravitational waves

TL;DR

This paper investigates how rotating gravitational waves can induce inertial frame rotation in a nearly flat spacetime, revealing that gravitational wave angular momentum influences inertial frames beyond stress-energy effects.

Contribution

It provides a first-order solution for gravitational wave-induced inertial frame rotation and demonstrates the role of gravitational wave angular momentum in Mach's principle.

Findings

Inertial frames rotate without time delay due to gravitational waves.

Gravitational wave angular momentum affects inertial frame rotation.

Mach's principle involves gravitational wave energy and angular momentum, not just stress-energy.

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.