Energy and Momentum Associated With a Static Axially Symmetric Vacuum Spacetime

Abstract

We use the Einstein and Papapetrou energy-momentum complexes to calculate the energy and momentum densities of Weyl metric as well as Curzon metric. We show that these two different definitions of energy-momentum complexes do not provide the same energy density for Weyl metric, although they give the same momentum density. We show that, in the case of Curzon metric, these two definitions give the same energy only when R → ∞. Furthermore, we compare these results with those obtained using Landau and Lifshitz, Bergmann and Møller.

Scalar field theory and energy-momentum problem of Yilmaz-Rosen metric in general relativity and teleparallel gravity

“…Gad, has investigated energy-momentum densities of a general static axially symmetric vacuum space-time, with the help of Landau-Lifshitz and Bergmann-Thomson energy-momentum complexes and found that these two definitions of energy momentum complexes do not provide the same energy density for the space-time (Gad 2006a(Gad , 2006b. However, M. Gad using the energy-momentum complexes of Einstein and Papapetrou calculated energy-momentum density of Weyl metric as well as Curzon metric and has showed that these two different definitions of energy-momentum complexes do not provide the same energy density for Weyl metric, although they give the same momentum density (Gad 2004a(Gad , 2004b(Gad , 2004c. Many researchers considered different energy-momentum complexes and obtained encouraging results (Radinschi and Grammenos 2006;Yang and Radinschi 2004;Sharif 2002Sharif , 2003Sharif , 2004aSharif , 2004bVagenas 2003aVagenas , 2003bVagenas , 2004Gad 2004aGad , 2004bGad , 2004cGad , 2006aGad , 2006b.…”

“…However, M. Gad using the energy-momentum complexes of Einstein and Papapetrou calculated energy-momentum density of Weyl metric as well as Curzon metric and has showed that these two different definitions of energy-momentum complexes do not provide the same energy density for Weyl metric, although they give the same momentum density (Gad 2004a(Gad , 2004b(Gad , 2004c. Many researchers considered different energy-momentum complexes and obtained encouraging results (Radinschi and Grammenos 2006;Yang and Radinschi 2004;Sharif 2002Sharif , 2003Sharif , 2004aSharif , 2004bVagenas 2003aVagenas , 2003bVagenas , 2004Gad 2004aGad , 2004bGad , 2004cGad , 2006aGad , 2006b. Virbhadra (1990Virbhadra ( , 1999, Virbhadra and Parikh (1993) investigated several space-times and showed that different energy-momentum complexes could provide exactly same results for a given space-time (Sharif and Fatima 2005).…”

Energy and momentum distributions of Kantowski and Sachs space–time

“…These results agree for the Schwarzschild, Vaidya and Janis-Newmann-Winicour space-times, but disagree for the Reissner-Nordström space-time. Many authors had similarly successfully applied the aforementioned energy-momentum complexes to various black hole configurations (Gad 2004a(Gad , 2004b(Gad , 2005a(Gad , 2006a(Gad , 2006b(Gad , 2006cVagenas 2003aVagenas , 2003bVagenas , 2004Vagenas , 2005Vagenas , 2006Yang et al 1997;Radinschi 1999Radinschi , 2000aRadinschi , 2000bRadinschi , 2000cRadinschi , 2000dRadinschi , 2000e, 2001aRadinschi , 2001bRadinschi , 2001cRadinschi , 2005Yang and Radinschi 2002, 2004Radinschi and Yang 2005;Radinski and Grammenos 2006;Yang 2000;Salti 2005, 2006;Salti 2005aSalti , 2005bSalti , 2005cSalti and Havare 2005;Havare et al 2006;Patashnick 2005;Grammenos 2005). …”

Energy and momentum associated with solutions exhibiting directional type singularities

“…Virbhadra [17] used Tolman, Landau-Lifshitz and papapetrou's prescriptions and found that they give the same energy and momentum densities for the aforementioned space-time and agree with the results obtained by using Einstein's prescription. In our previous two papers [39] we have calculated the energy and momentum densities associated with a general static axially symmetric vacuum space-time, using Einstein, Papapetrou and Møller's energy-momentum complexes. We found that these definitions do not provide the same energy density, while give the same momentum density.…”