Proposal for determining the energy content of gravitational waves by using approximate symmetries of differential equations

Ibrar Hussain, F. M. Mahomed, and Asghar Qadir
Phys. Rev. D 79, 125014 – Published 16 June 2009

Abstract

Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein’s field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to test particles. There have been various proposals to define the energy content, but they have not met with great success. Here we propose a definition using “slightly broken” Noether symmetries. We check whether this definition is physically acceptable. The procedure adopted is to appeal to “approximate symmetries” as defined in Lie analysis and use them in the limit of the exact symmetry holding. A problem is noted with the use of the proposal for plane-fronted gravitational waves. To attain a better understanding of the implications of this proposal we also use an artificially constructed time-varying nonvacuum metric and evaluate its Weyl and stress-energy tensors so as to obtain the gravitational and matter components separately and compare them with the energy content obtained by our proposal. The procedure is also used for cylindrical gravitational wave solutions. The usefulness of the definition is demonstrated by the fact that it leads to a result on whether gravitational waves suffer self-damping.

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  • Received 4 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.125014

©2009 American Physical Society

Authors & Affiliations

Ibrar Hussain1,*, F. M. Mahomed2,‡, and Asghar Qadir1,†

  • 1Centre for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology, Campus of the College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
  • 2Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics (DECMA), University of the Witwatersrand, Wits 2050, South Africa

  • *Correspondence should be addressed to ihussain@camp.edu.pk
  • aqadirmath@yahoo.com
  • Fazal.Mahomed@wits.ac.za

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Issue

Vol. 79, Iss. 12 — 15 June 2009

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