scholarly journals ENERGY CONTENTS OF GRAVITATIONAL WAVES IN TELEPARALLEL GRAVITY

2010 ◽  
Vol 25 (03) ◽  
pp. 221-232 ◽  
Author(s):  
M. SHARIF ◽  
SUMAIRA TAJ
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Gravitational Waves ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Conserved Quantities ◽  
Hamiltonian Approach ◽  
Momentum Fluxes

The conserved quantities, that are, gravitational energy–momentum and its relevant quantities are investigated for cylindrical and spherical gravitational waves in the framework of teleparallel equivalent of General Relativity using the Hamiltonian approach. For both cylindrical and spherical gravitational waves, we obtain definite energy and constant momentum. The constant momentum shows consistency with the results available in General Relativity and teleparallel gravity. The angular momentum for cylindrical and spherical gravitational waves also turn out to be constant. Further, we evaluate their gravitational energy–momentum fluxes and gravitational pressure.

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

scholarly journals Gravitational energy is well defined

2018 ◽  
Vol 27 (14) ◽  
pp. 1847017 ◽  
Author(s):  
Chiang-Mei Chen ◽  
Jian-Liang Liu ◽  
James M. Nester
Keyword(s):  
General Relativity ◽  
Large Class ◽  
Reference Frame ◽  
Linear Order ◽  
Local Density ◽  
Gravitational Energy ◽  
Local Energy ◽  
Hamiltonian Approach ◽  
Energy Value ◽  
Gravitating Systems

The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy–momentum is now regarded as quasi-local (associated with a closed 2-surface). We consider the pseudotensor and quasi-local proposals in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (i) many expressions, (ii) each depends on some nondynamical structure, e.g. a reference frame. The Hamiltonian approach gives a handle on both problems. Our remarkable discovery is that with a 4D isometric Minkowski reference, a large class of expressions — those that agree with the Einstein pseudotensor’s Freud superpotential to linear order — give a common quasi-local energy value. With a best-matched reference on the boundary, this value is the nonnegative Wang–Yau mass.

scholarly journals TELEPARALLEL GRAVITATIONAL ENERGY IN THE GAMMA METRIC

2006 ◽  
Vol 15 (05) ◽  
pp. 695-701 ◽  
Author(s):  
MUSTAFA SALTI
Keyword(s):  
General Relativity ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Coupling Constants ◽  
Dimensionless Coupling ◽  
Weinberg Complex

The Møller energy (due to matter and fields including gravity) distribution of the gamma metric is studied in teleparallel gravity. The result is the same as those obtained in general relativity by Virbhadra in the Weinberg complex and Yang–Radincshi in the Møller definition. Our result is also independent of the three teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.

scholarly journals ENERGY CONTENTS OF A CLASS OF REGULAR BLACK HOLE SOLUTIONS IN TELEPARALLEL GRAVITY

2010 ◽  
Vol 25 (38) ◽  
pp. 3241-3250 ◽  
Author(s):  
M. SHARIF ◽  
ABDUL JAWAD
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Teleparallel Gravity ◽  
Nonlinear Electrodynamics ◽  
Hamiltonian Approach ◽  
Regular Black Hole ◽  
Nonlinear Source ◽  
Teleparallel Theory ◽  
Black Hole Solutions

In this paper, we discuss the energy–momentum problem in the realm of teleparallel gravity. The energy–momentum distribution for a class of regular black holes coupled with a nonlinear electrodynamics source is investigated by using Hamiltonian approach of teleparallel theory. The generalized regular black hole contains two specific parameters α and β (a sort of dipole and quadrupole of nonlinear source) on which the energy distribution depends. It is interesting to mention here that our results exactly coincide with different energy–momentum prescriptions in general relativity.

Dirac Spin and Angular Momentum of the Stationary Axisymmetric Space-Time in the Teleparallel Gravity

2020 ◽  
Author(s):  
M F Mourad
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Axial Vector ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Special Cases ◽  
Vector Part ◽  
Dirac Spin

In the framework of teleparallel equivalent to general relativity, the stationary axisymmetric space-time in the teleparallel gravity for two different sets of tetrad fields have been investigated. For these sets, we have obtained the expressions for the torsion vector, torsion axial-vector and the angular momentum of the solution. We found that the obtained expressions of the torsion axial-vector and the angular momentum are, in general quite different in both two sets of tetrad fields, while the expressions for the torsion vector have the same value. Moreover, the vector part connected with Dirac spin has been evaluated as well. Finally, special cases of the stationary axisymmetric space-time are discussed.

scholarly journals GRAVITATIONAL ENERGY–MOMENTUM DENSITY IN BIANCHI TYPE II SPACE–TIMES

2006 ◽  
Vol 15 (04) ◽  
pp. 459-468 ◽  
Author(s):  
OKTAY AYDOGDU
Keyword(s):  
General Relativity ◽  
Energy Distribution ◽  
Total Energy ◽  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Momentum Density ◽  
Gravitational Energy ◽  
Type Ii ◽  
Rotationally Symmetric ◽  
Total Energy Distribution

In this paper, using Einstein, Landau and Lifshitz's energy–momentum complexes both in general relativity and teleparallel gravity, we calculate the total energy distribution (due to matter and fields, including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type II cosmological models. We show that energy densities in these different gravitation theories are the same, so they agree with each other. We obtain the result that the total energy is zero. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, Aydogdu and Saltı. Moreover, our result supports the viewpoints of Albrow and Tryon.

On the quantization of a neutron star

2020 ◽  
Vol 35 (09) ◽  
pp. 2050051 ◽  
Author(s):  
S. C. Ulhoa ◽  
E. P. Spaniol ◽  
H. G. V. Gonzalez ◽  
R. G. G. Amorim
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Neutron Star ◽  
Phase Space ◽  
Gravitational Energy ◽  
Weyl Quantization ◽  
Star Model ◽  
Quantum Equation ◽  
Classical Energy

This paper deals with quantum gravitation applied to a simple neutron star model. For the quantization process, we use the Weyl prescription that can be used for functions that are not defined in the phase space. The Weyl quantization is applied to the expression of gravitational energy defined in the context of Teleparallelism Equivalent to General Relativity (TEGR). From this, a quantum equation is obtained whose observable is the classical energy. As a consequence, we obtained discretizations for the mass of the star and its angular momentum.

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