The energy-momentum tensor of gravitational waves, Wyman spacetime and freely falling observers

A good definition for the energy momentum tensor of gravity (EMTG) in General Relativity (GR) is a hard, if not impossible, task. On the other hand, in its teleparallel version, known as The Teleparallel Equivalent of General Relativity (TEGR), one can define the EMTG in a very satisfactory way. In...

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Bibliographic Details
Published inarXiv.org
Main Author miga, J B
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.08.2018
Subjects
Falling
Flux density
Free fall
Gravitation
Gravitational waves
Mathematical analysis
Momentum
Observers
Physics - General Relativity and Quantum Cosmology
Relativity
Tensors
Theory of relativity
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Summary:A good definition for the energy momentum tensor of gravity (EMTG) in General Relativity (GR) is a hard, if not impossible, task. On the other hand, in its teleparallel version, known as The Teleparallel Equivalent of General Relativity (TEGR), one can define the EMTG in a very satisfactory way. In this paper, it is proved that the EMTG of TEGR for linearized gravitational waves (GWs) is the same as the version of GR that is usually given in the literature. In addition, the exact version of the EMTG for a \(pp-\)wave with a \(+\) polarization is obtained in a freely falling frame (FFF). Unlike the previous case, the energy density can be either positive or negative, depending on the details of the wave. The gravitational energy density for the Wyman spacetimes is obtained both in a static frame and in a FFF. It turns out that observers in free fall can measure the effects of gravity.
ISSN:2331-8422
DOI:10.48550/arxiv.1808.06237