Energy Distribution associated with Static Axisymmetric Solutions

Abstract

This paper has been addressed to a very old but burning problem of energy in General Relativity. We evaluate energy and momentum densities for the static and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen and the gamma metrics, belonging to the Weyl class. We apply four well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and M$\ddot{o}$ller to compute energy-momentum density components. We obtain that these prescriptions do not provide similar energy density, however momentum becomes constant in each case. The results can be matched under particular boundary conditions.

arXiv comment18 pages, accepted for publication in Astrophysics and SpaceScience

References in corpus (8)

• Pseudotensors and quasilocal energy-momentum
• A conformal scalar dyon black hole solution
• Møller energy of the nonstatic spherically symmetric metrics
• Energy and Momentum in Spacetime Homogeneous G$\ddot{o}$del-type Metrics
• Energy and Momentum of a Class of Rotating Gravitational Waves
• Energy and momentum associated with a Static Axially Symmetric Vacuum Space-Time
• Energy and Momentum of a Stationary Beam of Light
• Energy Distribution of a Gödel-Type Space-Time

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• Energy Contents of Some Well-Known Solutions in Teleparallel Gravity
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• Energy Distribution of a Regular Class of Exact Black Hole Solutions
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