Inertial frame rotation induced by rotating gravitational waves

Article

Inertial frame rotation induced by rotating gravitational waves

Lynden-Bell D.; Bičák J.; Katz J.

Class. Quantum Grav. 25, 165018 (2008)

Abstract

We calculate the rotation of the inertial frame 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 cannot be expressed in terms of the influence of the stress–energy–momentum tensor alone but must also involve influences of gravitational wave energy and angular momentum.

Institute authors

Bičák, Jiří

Supported by

GACR 202/06/0041 — Contemporary problems of general relativity and gravitation
LC06014 — Centrum teoretické astrofyziky
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@article{UTF337,
  author        = {Lynden-Bell D. and Bičák J. and Katz J.},
  title         = {{Inertial frame rotation induced by rotating gravitational waves}},
  journal       = {Class. Quantum Grav.},
  volume        = {25},
  pages         = {165018},
  year          = {2008},
  doi           = {10.1088/0264-9381/25/16/165018},
  eprint        = {http://arxiv.org/abs/0807.3077},
  archivePrefix = {arXiv},
  url           = {http://www.iop.org/EJ/abstract/0264-9381/25/16/165018},
}