Poincaré gauge theory from self-coupling

Poincaré gauge theory is derived from a linear theory by the method suggested by Gupta for deriving Einstein’s general relativity from the linear theory of a spin-2 field. Non-linearity is introduced by requiring that a set of tensor fields be coupled to the Noether currents of the Poincaré group (energy-momentum and spin).     

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.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

A(2)2 parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A⁽²⁾₂/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A⁽²⁾₂ parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy–momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two.     

The meaning of general covariance of einstein’s theory of gravity

The fundamental symmetry of Einstein’s theory of gravity is Lorentz-invariance which leads to a well defined energy-momentum tensor. This is also true for Maxwell’s theory of electromagnetism which has an additional symmetry due to its spin one, restmass zero character. Similarly, the spin two, restmass zero character of the gravitational field leads to an additional gauge symmetry that happens to be isomorphic to the concept of general covariance. The gauge-covariant energy-momentum tensor for gravitational interactions vanishes identically.     

Energy localization in general relativity: A new hypothesis

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman detector interacting with a plane gravitational wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis.     

Gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein’s equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation. The gravitational potential U(r) which determines the lensing is directly give by the rotation curve U(r) = −v ²(r). This allows to test general relativity on the scale of galaxies where dark matter is relevant.     

Exact solutions of the Bach field equations of general relativity

Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations B_αβ=0 or B_αβ=?T_αβ, where B_αβ denotes the Bach tensor and T_αβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds²=g_αβdx^αdx^β of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field g_αβ is coupled by B_αβ=?T_αβ to an electromagnetic field F_αβ=?F_αβ obeying the Maxwell equations or to a neutrino field ?A obeying the Weyl equations respectively. Among interesting new metrics ds² there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.     

The energy-momentum tensor in scalar and gauge field theories

A previous study of the energy-momentum tensor in ?⁴ theory and spontaneously broken non-Abelian gauge field theories is extended here to show finiteness to all orders in perturbation theory. Divergences of Green's functions Γ_μν^(j) (q; p₁, …, p_j) involving the energy-momentum tensor θ_μν and j particle fields are removed by counterterms of the ordinary Lagrangian plus a renormalization of the coefficient of the Callan-Coleman-Jackiw improvement term in θ_μν. Physically the extra renormalization means that the mean square “mass radius” of elementary spin zero particles must be specified from experiment.     

Gravitational two-body problem—A source theory viewpoint

An analysis of the semirelativistic gravitational two-body problem based on Schwinger's source theory is given. Our treatment is purely classical but nongeometrical. Only the large distance behavior of the gravitational stress tensor is seen to be relevant for order G² contributions. For a gravitational stress tensor that has a pure Newtonian form, only the traceless choice is seen to be consistent with Einstein's theory. We find results in agreement with the earlier results of Einstein, Infeld, and Hoffmann, and Barker and O'Connell for spin-2 graviton exchanges between Dirac particles, and with Börner, Ehlers, and Rudolph for spin precession in theories with arbitrary post-Newtonian parameter γ. The source approach clearly displays the analogy between gravitational interactions and classical electrodynamics. We also discuss the general relationship between the periastron advance and spin-precession frequencies for a class of gravitation theories. Brief estimates of the various spin-precession effects are given for the Hulse-Taylor pulsar.     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

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.     

Spin dynamics in general relativity

The energy-momentum tensor of a fluid composed of spinning particles is presented in a form that is structurally similar to that of a fluid with the energy flux q^a with respect to the fluid velocity u^a, isotropic pressure p and the trace-free anisotropic pressure π^ab. The effect of spin in the evolution of a shear free cosmological model with irrotational geodesic flow is considered.     

On the relevance of general relativity with torsion at highest matter densities and in microphysics

General relativity with spin and torsion (U ₄ -theory) is discussed. Conventional general relativity (GR) and U ₄ -theory cannot be distinguished with the present experimental techniques. At high matter densities and in microphysics, however, U ₄ -theory gives different answers. The former is interesting in connection with gravitational collapse and the singularity theorems, the latter with respect to the quantization of the gravitational field.Presented at the Seventh International Conference on Gravitation and Relativity, June 1974, Tel-Aviv, Israel. Read by Prof. R.F. O'Connell, Louisiana State University.     

Localization of gravitational energy

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained.     

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     

The Momentum Four-Vector in Brans–Dicke Wormholes

In this work, in order to compute energy and momentum distributions (due to matter plus fields including gravitation) associated with the Brans–Dicke wormhole solutions we consider Møller’s energy-momentum complexes both in general relativity and the teleparallel gravity, and the Einstein energy-momentum formulation in general relativity. We find exactly the same energy and momentum in three of the formulations. The results obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling parameter, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum. (c) The results calculated supports the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of matter and all non-gravitational fields.