Gravitational Energy in Van Stockum Space-Time

Abstract

The purpose of this paper is to illustrate the problem of energy and momentum distributions of Van Stockum space-time within the framework of two different theories of gravity, general relativity and teleparallel gravity. We have shown that for all homogeneous space-times with metric components $g_{\mu \nu }$ being functions of time variable, $t$, alone and independent of space variables the total gravitational energy for any finite volume is identically zero. By working with general relativity, we have calculated the energy-momentum density for Van Stockum space-time using double index complexes and in the framework teleparallel gravity, we used the energy-momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. In our analysis, we sustained that general relativity and teleparallel gravity are equivalent theories of space-time under consideration. For space-time under consideration, we have shown that different complexes of energy-momentum density do not provide the same results neither in general relativity nor in teleparallel gravity.

arXiv comment16 pages No figures, Accepted for publication in Indian journal of physics (2021)

References in corpus (21)

• Gravitational Lorentz Force and the Description of the Gravitational Interaction
• Gravitational Energy-Momentum Density in Teleparallel Gravity
• Energy and angular momentum of charged rotating black holes
• Energy Distribution in 2d Stringy Black Hole Backgrounds
• Axial-Vector Torsion and the Teleparallel Kerr Spacetime
• Energy distribution in a BTZ black hole spacetime
• Energy-momentum complexes in f(R) theories of gravity
• Energy distribution in the dyadosphere of a Reissner-Nordstrom black hole in Moller's prescription
• Møller energy of the nonstatic spherically symmetric metrics
• Energy Distribution of a Charged Regular Black Hole
• Riemannian and Teleparallel Descriptions of the Scalar Field Gravitational Interaction
• Energy Distribution of a Stringy Charged Black Hole
• Energy of a Conformal Scalar Dyon Black Hole
• Energy and momentum associated with a Static Axially Symmetric Vacuum Space-Time
• Energy Distribution of a Stationary Beam of Light
• Energy Distribution of a Gödel-Type Space-Time
• Energy distribution of the Einstein-Klein-Gordon system for a static spherically symmetric spacetime in (2+1)-dimensions
• On the energy of charged black holes in generalized dilaton-axion gravity
• Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities
• Energy and Momentum Distributions of Kantowski and Sachs Space-time
• Goedel type solution in teleparallel gravity