The Brans-Dicke scalar field in Einstein-Cartan theory

In the framework of Einstein-Cartan (EC) theory, the Brans-Dicke (BD) theory is considered and it is found that a scalar field nonminimally coupled to the gravitational field gives rise to torsion, even though the scalar field has zero spin. The metric equations stay the same if the coupling constant is rescaled, but the equations of motion of a test particle, derived from the conservation equations, differ from those of the usual BD theory without torsion. The gravitational red-shift value differs considerably from the usual prediction of general theory of relativity (GTR), and rules out the possibility of a torsion version of BD theory for<6.     

Theory of fiber bundle with local metric of internal space and gravitation with torsion

In this paper we propose a new theory of a fiber bundle provided with a local metric of internal space. The fibers differ from usual fibers, having an enlarged factor. The enlargement may be procured by a differential mapping(x) from structure groupG to the fiberF _x atx M, and(x)R. The torsion presented stems from the local metric of internal space and the local metric stems from a induced mapping _*(x) of(x). From the theory we can get the Brans-Dicke theory with torsion. If we assume the spin density of the gauge field determines the enlarged factor of the fiberF _x, our theory is an extended Cartan theory.     

Inflation in Brans-Dicke theory for the radiation universe

The Brans-Dicke (BD) theory admits de Sitter spacetime as a solution with an equation of statep=1/3 when the coupling constant of the BD theory is –3/2.     

Cosmological models with constant deceleration parameter in Brans-Dicke theory

A detailed study of cosmological models with constant deceleration parameterq is undertaken in the framework of Brans-Dicke theory. These models are divided into two categories: (i) singular models with expansion driven by big-bang impulse, (ii) non-singlar models with expansion driven by creation of matter particles. Prigogine's hypothesis of creation of matter out of gravitational energy is analysed and extended to BD cosmology. To accommodate the creation of new particles, the universe is regarded as an open thermodynamical system and the energy conservation equation is modified with the incorporation of a creation pressure termp _c in the energy-momentum tensor . The exact solutions of the field equations of BD theory with are obtained using the power law relation=KR , which leads to models with constantq. The behaviour of the solutions is investigated for different range of values ofa. The role played by the BD scalar field and creation of matter particles in the expansion of the universe is investigated. It is found that one particular model with constantq has exponential expansion.     

Extended inflation in higher-dimensional spacetime with a Brans-Dicke scalar field

Starting from an assumption of homogeneity of matter-energy tensor and Brans-Dicke (BD) scalar field we obtain a Robertson-Walker type of metric form in five-dimensional spacetime with the essential difference that our model is spatially inhomogeneous. The model exhibits an interesting feature in that as we approach the centre of symmetry the compact dimension becomes very large, with the implication that the Kaluza-Klein excitations become very light when located there and that the origin may represent a singular concentration of matter with motion in the extra dimension. Following Wesson the effective 4D properties of matter from the 5D vacuum solutions are also briefly discussed. Assuming particular functional relationships between and as also between the scale factor and scalar field, we obtain exact solutions which may be of relevance to the early universe and its extended inflation in the BD type of theory. We also discuss very briefly rollover time immediately after tunneling to the true vacuum state to explore if dimensionality has any marked influence on the situation.     

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant ₀ with respect to the value –3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in the presence of a massive scalar field having a positive energy density.     

Dynamical structure of linearizedGL(4) gravities

The physical content of the three more natural models ofGL(4) gravity is analyzed, for the case of weak fields. The first model we deal with is the linearized version of Yang's onetensor-field gravity. It is shown that this is a scalar-tensor theory, with its scalar part contained in the symmetric tensorh , instead of appearing explicitly, externally to the symmetric tensorh , as happens in Brans-Dicke type of scalar-tensor theories. The second and the third linearized models, which can both be derived from the fourth-order action postulated by Yang, turn out to be two-tensor decoupled systems. In both cases one of the tensors is the symmetric weak metric gravity tensor field. The second tensor appearing in these two models, representing theGL(4)-gauge field, is either a linearized symmetric affinity (in the second model) or a linearized but nonsymmetric affinity (for the third model). It is shown that in these last two cases the affinity contains a helicity-3 propagating field. The connection is also given between the fourth-order system which determines the dynamical structure (for the last two models) of the metric tensor and the third-order Yang model of gravity. Owing to the presence of helicity-3 fields we show that it is better to regard Yang's action as an action for a two-tensor system instead of trying to recover from it a pure gravity (one-tensor-field) action. Finally, it is shown what is the dynamical structure of the second and third linearized two-tensor models which can be derived from Yang's action.On leave of absence from the Universidad Simón Bolívar.     

Mach's principle. Part 2. Realization of Dirac's hypothesis in Brans-Dicke theory with cosmological term

Brans-Dicke theory supplemented with the scalar field potential of the formm ⁶/ Gm ₆ enables one to realize Dirac's big numbers hypothesis.     

Kerr-type solution in Brans-Dicke theory

The Kerr-type solution in the Brans-Dicke theory should contain three parameters: a massm, a rotational parametera ₀, and a coupling parameter It goes over to the Kerr solution in Einstein's theory of general relativity in the limit 8. Using these conditions, we construct a special solution from Bruckman's solutions which can be regarded as a Kerr-type solution in the Brans-Dicke theory.     

Conformal invariance and torsion in general relativity

We study a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition g =0. A scalar field is added to the theory, and a conformally invariant action integral, linear in the curvature tensor, is defined. The linear connections emerging from the variational principle contain torsion that is related to a propagating spin-1 vector field, identified as the electromagnetic gauge potential. We obtain a set of conformally invariant equations for the metric field, and conclude that Einstein's equations arise from a particular choice of gauge. Finally, spin-1/2 fields are introduced by means of the vierbein formalism, and the qualitative features of the theory are maintained.     

Static perfect fluid in Brans-Dicke theory

The static perfect fluid in Brans-Dicke theory with spherical symmetry and conformal flatness leads to a differential equation in terms of the scalar field only. We obtain a unique exact solution for the casep=, but density and pressure are singular at the center. We further consider the metric corresponding to a static nonrotating space-time with two mutually orthogonal spacelike Killing vectors in Brans-Dicke theory. We obtain a differential equation involving only the scalar field for the equation of statep= The general solution is found as a transcendental function. Finally, we generalize a theorem given by Bronnikov and Kovalchuk (1979) for perfect fluid in Einstein's theory.On leave from Jadavpur University, Calcutta-32, India.     

Classical gravity and quantum matter fields in unified field theory

The Einstein-Schrödinger purely affine field theory of the non-symmetric field provides canonical field equations without constraints. These equations imply the Heisenberg-Pauli commutation rules of quantum field theory. In the Schrödinger gauging of the Einstein field coordinatesU _kl ⁱ = _kl ⁱ – _l ⁱ _km ^m , this unified geometric field theory becomes a model of the coupling between a quantized Maxwellian field in a medium and classical gravity. Therefore, independently of the question as to the physical truth of this model, its analysis performed in the present paper demonstrates that, in the framework of a quantized unified field theory, gravity can appear as a genuinely classical field.     

On a Mechanical Model of the Bopp-Podolsky Potential

For an arbitrary given distribution of dislocations and disclinations the general state of stress of a mechanical continuum is investigated. The medium is reacting with stresses and momentum stresses (Cosserat continuum). By means of differential geometry it is shown that the deformations _ik and ?_ik of two arbitrary materials with identical distributions of defects differ merely by a displacement field u_i(x^r, t). If _ik are the eigendeformations of an isotropic medium, then in the linear theory the field u_i of a Cosserat continuum can be separated from _ik. If the problem is static the u_i obey the potential equation of Bopp-Podolsky electrodynamics. As source only torsion (dislocations and torsion of disclinations) is acting. To give an example the field u_i for straight dislocations and disclinations is calculated. Especially the problem of singularities is discussed.     

An application of functional equations to the analysis of the invariance identities of classical gauge field theory

The equations of motion for a particle in a classical gauge field are derived from the invariance identities ² and basic assumptions about the Lagrangian. They are found to be consistent with the equations of some other approaches to classical gauge-field theory, and are expressed in terms of a set of undetermined functions E. The functions E are found to satisfy a system of differential equations which has the same formal structure as a system of equations from Yang-Mills theory. ³ These results are obtained by a new method which applies techniques from the theory of functional equations to deduce the way in which the arguments of the Lagrangian must combine. The method constitutes an aid for obtaining the equations of motion when a non-gauge-invariant Lagrangian is chosen, and it is assumed that the equations of motion can be written in a gauge-invariant manner.     

The physics of detecting torsion and placing limits on its effects

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,(8G/c ²)( ²/4). The best way of maximizing the total interaction energy is to increase the spin density of the source _s, and, at the same time the spin numberS _D of the detector.This essay was awarded an honorable mention in 1984 by the Gravity Research Foundation—Ed.     

Direct gauging of the Poincaré group

Realization of the Poincaré group as a subgroup ofGL(5,R) that maps an affine set into itself is shown to lead to a well-defined minimal replacement operator when the Poincaré group is allowed to act locally. The minimal replacement operator is obtained by direct application of the Yang-Mills procedure without the explicit introduction of fiber bundle techniques. Its application gives rise to compensating 1-formsW , 1 6, for the local action of the Lorentz groupL(4,R), and to compensating 1-forms ^k , 1k4, for the translation groupT(4). When applied to the basis 1-formsdx ⁱ of Minkowski space, distortion 1-formsB ^k result that define a canonical anholonomic coframe that contains both theT(4) and theL(4,R) compensating fields. When the canonical coframe is considered as a differential system onM ₄, it gives rise to gauge curvature expressions and Cartan torsion, but the latter has important differences from that usually encountered in the associated literature in view of the inclusion of the compensating fields forL(4,R). The standard Yang-Mills minimal coupling construct is used to obtain a total Lagrangian. This leads to a system of field equations for the matter fields, theT(4) compensating fields, and theL(4,R) compensating fields. Part of the current that drives theT(4) compensating fields is the 3-form of gauge momentum energy that obtains directly from the momentum-energy tensor of the matter fields onM ₄ under minimal replacement. Introduction of the Cartan torsion in the free-field Lagrangian is shown to lead to a direct spin decoupling in the sense that the gauge momentum energy (orbital) contribution of the matter fields to the spin current is eliminated. Explicit conservation laws for total momentum energy current and total spin current are obtained.     

Wormholes in vacuum Brans-Dicke theory

We present a Euclidean wormhole solution in vacuum Brans-Dicke theory, which is different from that obtained by Accetta et al. This wormhole appears to have the feature that its throat dimension increases linearly with Euclidean cosmic time, although this increase may not be measurable. It also requires a negative Brans-Dicke parameter.     

Direct gauging of the Poincaré group. II

This paper continues the study of direct gauge theory of the Poincaré groupP ₁₀. The meanings and implications of transformations induced by the local action ofP ₁₀ are studied, and transformation rules for all field quantities are derived for the local action ofP ₁₀ in a sufficiently small neighborhood of the identity. These results lead directly to a system of fundamental partial differential equations that are both necessary and sufficient for invariance of the free field Lagrangian density. Homogeneity arguments and the classical theory of invariants are used to obtain the most general free field Lagrangian density. Gauge conditions are shown to imply coordinate conditions, and an algebraic system of antiexact gauge conditions is implemented. The underlying Minkowski space,M ₄, and the resulting Riemann-Cartan space,U ₄, become attached at their centers, as do their respective frame and coframe bundles. Weak constraints of vanishing torsion are studied. All field quantities are shown to be determined in terms of the compensating l-forms for the Lorentz sector alone provided an explicit system of integrability conditions is satisfied. Field equations of the Einstein type are shown to result.     

Spin and torsion in general relativity II: Geometry and field equations

From physical arguments space-time is assumed to possess a connection is Christoffel's symbol built up from the metric g _ij and already appearing in General Relativity (GR). Cartan's torsion tensor and the contortion tensor K _ij ^k , in contrast to the theory presented here, both vanish identically in conventional GR. Using the connection introduced above, in this series of articles we will discuss the consequences for GR in the framework of a consistent formalism. There emerges a theory describing in a unified way gravitation and a very weakspin-spin contact interaction. In Part I of this work† we discussed the foundations of the theory. In this Part II we present in section 3 the geometrical apparatus necessary for the formulation of the theory. In section 4 we take the curvature scalar (or rather its density) as Lagrangian density of the field. In this way we obtain in subsection 4.1 the field equations in their explicit form. In particular it turns out that torsion is essentially proportional to spin. We then derive the angular momentum and the energy-momentum theorems (subsections 4.2-4); the latter yields a force proportional to curvature, acting on any matter with spin. In subsection 4.5 we compare the theory so far developed with GR. Torsion leads to a universal spin-spin contact     

Development of the Sachs Theory of Electrodynamics

The most general form of electrodynamics has been derived by Sachs [1] from the irreducible representations of the Einstein group. In this paper the Sachs theory is developed as a gauge theory with a vacuum four-current i _j . The B Cyclic Theorem O(3) electrodynamics is derived from a consideration of four-vectors appearing in the Sachs theory, and electromagnetic helicity, expressed in terms of the B ⁽³⁾ field of O(3) electrodynamics, is derived from the more general Sachs theory.