Energy-momentum distribution of the Weyl-Lewis-Papapetrou and the Levi-Civita metrics

Abstract

This paper is devoted to compute the energy-momentum densities for two exact solutions of the Einstein field equations by using the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller. The spacetimes under consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The Levi-Civita metric provides constant momentum in each prescription with different energy density. The Weyl-Lewis-Papapetrou metric yields all the quantities different in each prescription. These differences support the well-defined proposal developed by Cooperstock and from the energy-momentum tensor itself.

Teleparallel Energy–momentum Distribution of Static Axially Symmetric Spacetimes

“…Vargas [32] found that the total energy of the closed Friedmann-Robertson-Walker spacetime is zero by using teleparallel version of Einstein and Landau-Lifshitz complexes which agreed with the results of GR [37]. Recently, Sharif and Jamil [38] evaluated the energy-momentum distribution of Lewis-Papapetrou spacetime by using Möller's prescription and found that the results of TPG and GR [39] are not consistent.…”

“…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.…”

“…Salti and his co-workers [33][34][35][36] considered some particular spacetimes and calculated energy-momentum densities by using different prescriptions both in GR and TPT and found the similar results. Recently, Sharif and Amir [38] evaluated the energy-momentum distribution of Lewis-Papapetrou spacetimes by using the TP version of Möller's prescription and found that the results do not agree with those available in the context of GR [39]. In this paper, we investigate energy-momentum distribution for the Weyl metrics in the context of the TPT.…”

Energy contents of some rotating spacetimes in teleparallel gravity

“…and furnished consistent results of energy density for gravitational waves, static and non-static cosmic string spacetimes by applying different prescriptions. However, inconsistent results (Gad 2004(Gad , 2006Sharif andFatima 2005, 2006) were obtained for the Weyl metrics.…”

“…In this framework, Maluf et al (2002) defined gravitational energy, momentum and angular momentum using the literature (Maluf 1994). Adopting this procedure, many people (Maluf et al 2003;da Rocha-Neto and Castello-Branco 2003;Sharif andTaj 2010a, 2010b) computed energy and its contents for different solutions. Recently, we have also investigated energy and its relevant quantities for a class of regular black holes coupled with non-linear electrodynamics source (Sharif and Jawad 2010).…”