2009/03/11 by Ibrar Hussain, F. M. Mahomed, Asghar Qadir · 20 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Content (measure theory) #Einstein #Einstein field equations #Energy (signal processing) #Geometry #Gravitation #Gravitational field #Gravitational wave #Homogeneous space #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Noether's theorem #Nonlinear Waves and Solitons #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Symmetry (geometry) #Theoretical physics #gr-qc
paper · pdf · doi:10.1103/physrevd.79.125014
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 79(12) (American Physical Society) · 26 pages, 6 figures
arxiv created 2009/03/11 · openalex publication_date 2009/06/16 · arxiv updated 2010/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.