Charged dilaton,energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity

We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR). The spacetime of these tetrad fields is the charged dilaton. Our results show that the energy associated with one of these tetrad fields is consistent, while the other one does not show this consistency. Therefore, we use the regularized expression of the gravitational energy-momentum tensor of the TEGR. We investigate the energy within the external event horizon using the definition of the gravitational energy-momentum. PACS 04.70.Bw; 04.50.+h; 04.20.-Jb     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field,with two unknown functions of radial coordinate,in the framework of a teleparallel equivalent of general relativity(TEGR).The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordstrm black hole.We also calculate the spatial momentum and angular momentum.     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity (TEGR). The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordström black hole. We also calculate the spatial momentum and angular momentum.     

Gravitational radiation fields in teleparallel equivalent of general relativity and their energies

We derive two new retarded solutions in the teleparallel theory equivalent to general relativity (TEGR).One of these solutions gives a divergent energy.Therefore,we use the regularized expression of the gravitational energymomentum tensor,which is a coordinate dependent.A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.     

Tetrad Fields,Reference Frames,and the Gravitational Energy–Momentum in the Teleparallel Equivalent of General Relativity

The concept and definitions of the energy–momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR) are reviewed. The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenböck connection. Second, in the phase space of the TEGR there exists an algebra of the Poincaré group. Not only the definitions of the gravitational energy–momentum and 4-angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, numerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review, the concept of localizability of the gravitational energy is revisited, in light of results obtained in recent years. The behavior of free particles is studied in the space–time of plane fronted gravitational waves (pp-waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp-waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. This theoretical result is considered an important and definite argument in favor of the localization of the gravitational energy–momentum, and by extension, of the gravitational 4-angular momentum.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy--momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy--momentum we obtain the value of energy.     

Metric‐free definition of the energy momentum tensor: Gravitation with symmetric connection

A metric‐free definition of the energy momentum tensor is presented. That definition can be used with any Lagrangian based gravitational theory where the independent variable is a symmetric connection. The case of Hilbert‐Einstein gravitation is treated as an example of such a theory.     

Fermion Fields,Boson Fields,and Gravitational Field

If a tetrad theory is derivable from a variational principle with a Lagrangian ?? of the form ?? = ??_F+??_M 6 tetrad components will be defined by the vacuum equations if the energy momentum tensor is symmetric. Therefore, we look for a realisation of a programme proposed in a little different way by TREDER according to which the 16 tetrad field equations should degenerate to 10 equations for the Riemannian metric if boson fields are the only source of the gravitational field.     

General regular charged space-times in teleparallel equivalent of general relativity

Using a non-linear version of electrodynamics coupled to the teleparallel equivalent of general relativity (TEGR), we obtain new regular exact solutions. The non-linear theory reduces to the Maxwell one in the weak limit with the tetrad fields corresponding to a charged space-time. We then apply the energy-momentum tensor of the gravitational field, established in the Hamiltonian structure of the TEGR, to the solutions obtained.     

Five-dimensional teleparallel theory equivalent to general relativity, the axially symmetric solution, energy and spatial momentum

A theory of (4+1)-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields (pentad), defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.     

Do gravitational waves carry energy‐momentum and angular momentum?

We show that gravitational waves which possess a non‐vanishing Riemann tensor R_iklm ≠ 0 always carry energy‐momentum and angular momentum. Our proof uses canonical superenergy and supermomentum tensors for the gravitational field.     

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of(N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity(TEGR).The fundamental gravitational field variables are the(N+1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution(Schwarzschild(4+1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.     

The teleparallel equivalent of general relativity

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.     

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity.The fundamental field variables are the tetrad fields e i μ and the gravity is attributed to the torsion.A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived.The energy associated with this solution is calculated using the two-dimensional gravitational energy-momentum formula.     

On the gravitational angular momentum of rotating sources

The gravitational energy–momentum and angular momentum satisfy the algebra of the Poincaré group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy–momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.     

Hawking radiation from gravity''s rainbow via gravitational anomaly

Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigates Hawking radiation from the modified Schwarzschild black hole from gravity＇s rainbow from the anomaly point of view. Unlike the general Schwarzschild space-time, the metric of this black hole depends on the energies of probes. The obtained result shows to restore the underlying general covariance at the quantum level in the effective field, the covariant compensating flux of energy-momentum tensor, which is related to the energies of the probes, should precisely equal to that of a （1 ＋ 1）-dimensional blackbody at the Hawking temperature.     

Traces of products of angular momentum operators

Traces of products of angular momentum operators in a spherical or cartesian basis are common in the theory of atomic levels in fields, in the theory of nuclear orientation and of asymmetric top moments. Conventional angular momentum techniques lead to difficult and cumbersome calculations. In the present paper Schwinger's coupled boson representation is used in straightforward calculations of angular momentum and spherical tensor traces, of matrix elements and of asymmetric top moments. Only simple algebra, elementary multiplication and summation of integers are necessary. The method considerably simplifies calculations with angular momentum operators.     

Spin matrices for gravitons and the humblet decomposition of the angular momentum of gravitational radiation in the linearized theory

We develop spin matrices for a classical gravitational field in the linearized theory which satisfy angular-momentum commutation relations and are appropriate for a spin angular momentum of two. The same spin matrices come out of a decomposition of the angular momentum density of the linearized gravitational field into orbital and spin parts, similar to that carried out by Humblet for the electromagnetic field. To achieve this decomposition, we use the momentum density for the gravitational field obtained from the Landau-Lifshitz pseudo-tensor in the weak gravity limit. We note a formal connection between the spin angular momenta of gravitational and electromagnetic fields using the Kaluza-Klein idea.