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

Abstract

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.

14 pages

References in corpus (5)

• The teleparallel equivalent of general relativity
• On the covariance of teleparallel gravity theories
• Is Teleparallel Gravity really equivalent to General Relativity?
• Variations of the Energy of Free Particles in the pp-Wave Spacetimes
• Wormholes in Wyman's solution

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• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Conformal Teleparallel Theories and Weyl Geometry
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• On the gravitational energy problem and the energy of photons
• Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• The meaning of torsion in teleparallel theories
• Gravitational Energy Creation in the Sandwich pp-Waves Collision
• Gravitational energy in pp-wave spacetimes