The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

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.     

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.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) 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 apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

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.     

Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ²-2mAξ³-q²A²ξ⁴. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ²)(1+r₊Aξ)(1+r_-Aξ) with r_± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.     

Variables suitable for constructing quantum states for the teleparallel equivalent of general relativity I

We present the first part of an analysis aimed at introducing variables which are suitable for constructing a space of quantum states for the Teleparallel Equivalent of General Relativity via projective techniques—the space is meant to be applied in a canonical quantization of the theory. We show that natural configuration variables on the phase space of the theory can be used to construct a space of quantum states which however possesses an undesired property. We introduce then a family of new variables such that some elements of the family can be applied to build a space of quantum states free of that property.     

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity(TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed.     

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     

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.     

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.     

Geodesically equivalent metrics in general relativity

We discuss whether it is possible to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are nonparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric from its nonparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorentz signature.     

Conformally equivalent metrics in bimetric general relativity

Space-times conformal to physical space-time are considered, assuming the nongravitational energy is conservative after the conformal transformation. Necessary and sufficient conditions satisfied by the conformal factor axe found for a given type of transformation of the energy tensor. The weak gravitational field is defined and the coordinate conditions for the existence of conformal factors in such a field are obtained.     

Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum

The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.     

Optical scalars for conformally equivalent spaces in the general theory of relativity

We obtain and investigate relationships between the optical scalars (expansion, rotation, shear) of isotropic congruences in conformally related spaces.     

The regimen of general relativity

New developments in our understanding of the electron-atom collision process have been made possible by combining the use of highly monochromatic electron beams and intense CO₂ lasers. This paper reviews such experiments and discusses possible future progress in what is a new field in atomic collision physics.     

The gauge in general relativity

The view is taken that the field equations of General Relativity, without a definition of congruence of length and time intervals at different events, are without physical content. The possibility is explored that the customary Einstein field equations are to be used but with a different congruence definition than is customary. When these resulting equations are, in turn, expressed with the customary congruence, they comprise a new set of field equations physically not equivalent to either Einstein's or Brans-Dicke's formulations of general relativity. Similarities with Einstein's and Brans-Dicke's formulations are discussed, and the possibility of experimental confirmation of these new equations is also briefly considered.     

The variational principle of general relativity

It is shown that the field equations of general relativity never afford a minimum or maximum-not even locally-to the action integralI. Solutions of the field equations always represent a stationary value ofI.     

The charged line-mass in general relativity

The two exterior solutions for a charged line-mass are examined. In both cases the mass per unit length is negative.