Teleparallel version of the stationary axisymmetric solutions and their energy contents

Abstract

This work contains the teleparallel version of the stationary axisymmetric solutions. We obtain the tetrad and the torsion fields representing these solutions. The tensor, vector and axial-vector parts of the torsion tensor are evaluated. It is found that the axial-vector has component only along ρ and z directions. The three possibilities of the axial vector depending on the metric function B are discussed. The vector related with spin has also been evaluated and the corresponding extra Hamiltonian is furnished. Further, we use the teleparallel version of Möller prescription to find the energy-momentum distribution of the solutions. It is interesting to note that (for λ = 1) energy and momentum densities in teleparallel theory are equal to the corresponding quantities in GR plus an additional quantity in each, which may become equal under certain conditions. Finally, we discuss the two special cases of the stationary axisymmetric solutions.

The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

“…The (ELLPW), BergmannThompson and Møller prescriptions yield meaningful results in the case of 2 and 3 dimensional space-times [90][91][92][93]. We also point out another interesting issue, the similarity of results which were obtained for many geometries using both energy-momentum definitions and the teleparallel gravity theory [45][46][47][48][49][50][51][52][53][54][55]. Whereas Chang, Nester and Chen [30] demonstrated in their studies that the energy-momentum complexes can be considered actually quasi-local and legitimate expressions for the energy-momentum.…”

“…Many scientist worked at this issue, using different definitions, like superenergy tensors [24][25][26][27][28][29], quasi-local mass definitions [30][31][32][33][34][35][36][37][38], pseudotensorial prescriptions, and here we notice the energy-momentum complexes of Einstein [14][15][16], Landau-Lifshitz [39], Papapetrou [40][41][42], Weinberg [17][18][19] (ELLPW), Bergmann-Thomson [43], Qadir-Sharif [44] and Møller [20], and teleparallel gravity theory [45][46][47][48][49][50][51][52][53][54][55]. The pseudotensorial definitions, except the Møller energy-momentum complex, imply to performed the calculations using non-covariant, coordinate dependent expressions, and yields acceptable results only in the case of quasi-Cartesian coordinates.…”

Teleparallel Energy-Momentum Distribution of Spatially Homogeneous Rotating Spacetimes

“…They proved that the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field in the case of slow rotation and weak field approximations. In previous papers [51,[61][62][63], we have found the TP versions of the Friedmann models, Lewis-Papapetrou spacetimes, stationary axisymmetric Einstein-Maxwell solutions and also discussed the energy-momentum distribution in last three papers. The problem of localization of energy has been reconsidered, in the frame work of TPG, by many scientists.…”

“…Currently [61][62][63], we considered some particular spacetimes and calculated the energymomentum densities and found that the results disagree in general but can coincide under certain conditions. In this paper, we extended the work and explore the energy-momentum distribution of spatially homogeneous rotating spacetimes by using the TP version of Möller's prescription.…”

A non-diagonal singularity-free model in torsion gravity

“…In the literature, there are many interesting studies for teleparallel gravity available where the authors have discussed the exact solutions of space-time models and compared their results with those obtained in general relativity [1][2][3][4][5][6][7][8][9]. Recently, Pereira et al [10] by performing the Schwarzschild and the stationary axisymmetric Kerr solutions in torsion gravity, attested that, the axial-vector torsion could be taken as the gravitomagnetic component of the gravitational field under the weak field approximation and the slow rotation case.…”