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, Papapetrou and Möller to compute energymomentum 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.

Teleparallel Energy–momentum Distribution of Static Axially Symmetric Spacetimes

“…If we take γ ρ e γ = −2ρψ z 2 then energy also becomes constant which coincides with the energy in GR [40][41][42]. It is worth mentioning here that the results are independent of the coupling constant λ, that is, these results are valid for any teleparallel theory.…”

“…In recent papers [26][27][28][39][40][41][42], Sharif and his collaborators used different prescriptions to determine the energy-momentum distribution for various spacetimes in GR. These results do not coincide for any of the prescriptions.…”

“…Further, it has been extended to the special case as a Curzon metric. We also compare our results with [40][41][42] in the context of GR.…”

Energy Momentum of Marder Universe in Teleparallel Gravity

“…Virbhadra and his collaborators have considered many space-time models and showed that several energy-momentum complexes give the same and acceptable results for a given space-time model [1, 13-16, 36-50, 66-70, 72-75], Virbhadra [73], using the general relativity versions of energy and momentum complexes of Einstein, Landau-Lifshitz, Papapetrou and Weinberg's for a general non-static spherically symmetric metric of the Kerr-Schild class, showed that all of these energy-momentum formulations give the same energy distribution as in Penrose energy-momentum complex. Sharif et al [58][59][60][61][62][63] have investigated in detail energy-momentum problem in the theory of general relativity and teleparallel gravity by using different space times and different definitions. Albrow [2] and Tryon [65] suggested that in our universe, all conserved quantities have to vanish.…”

Energy Contents of the Wormholes

“…While many definitions are coordinate dependent, but one of them, the Møller energy-momentum definition, is not. 10 Except for the Møller definition, these energy-momentum definitions give meaningful results, when they are performed "Cartesian" coordinates. Contrary to the condition, Møller energy-momentum complex are used in any coordinate system.…”