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.     

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.     

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.     

Bianchi type-I solutions for modified Brans-Dicke cosmology

Cosmological dust solutions have been obtained in Bianchi type-I homogeneous space for Brans-Dicke modified theory by the condition of the cosmological parameter ().     

Raychaudhuri's equation and the present universe in Brans-Dicke theory

Raychaudhuri's equation for the Brans-Dicke theory is used to relate/G to the deceleration and the density parameters.     

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.     

Exact solutions in Brans-Dicke theory with bulk viscosity

The effect of bulk viscosity on the evolution of the homogeneous and isotropic cosmological models in the Brans-Dicke theory of gravitation is studied. Solutions are found, with a baratropic equation of state, a time-independent bulk viscosity, the gravitational constant inversely proportional to the age of the universe, and the mass of the universe (in the closed model) proportional to the square of its age; the expansion factor is a linear function of the cosmological time. For flat space, power law expansions are found, among them one that is related to extended inflation.     

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.     

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.     

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.     

A parity-violatingU 4-gravitation theory

The general structure of a metric-torsion theory of gravitation allows a parity-violating contribution to the complete action which is linear in the curvature tensor and vanishes identically in the absence of torsion. The resulting action involves, apart from the constant ¯K _E =8/c⁴, a coupling (B) which governs the strength of the parity interaction mediated by torsion. In this model the Brans-Dicke scalar field generates the torsion field, even though it has zero spin. The interesting consequence of the theory is that its results for the solar-system differ very little from those obtained from Brans-Dicke (BD) theory. Therefore the theory is indistinguishable from BD theory in solar-system experiments.     

The limits of Brans-Dicke spacetimes: a coordinate-free approach

We investigate the limit of Brans-Dicke spacetimes applying a coordinate-free technique. We obtain the limits of some known exact solutions. It is shown that these limits may not correspond to similar solutions in the general relativity theory.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Cylindrically symmetric Zel'dovich fluid distributions in general theory of relativity

The problem of charged perfect fluid distribution is investigated when the space-time is described by the Einstein-Rosen metric. It is shown that with assumed cylindrical symmetry the cosmological constant vanishes, the electromagnetic field becomes source-free, and the perfect fluid reduces to Zel'dovich fluid withp=. Sets of exact solutions for this case have been obtained and the corresponding solutions for Brans-Dicke-Maxwell fields have been derived. For these solutions the Einstein-Rosen metric, however, goes over to three-parameter Marder metric in Brans-Dicke theory.     

Brans-dicke vacuum solutions and the cosmological constant: A qualitative analysis

We investigate Brans-Dicke vacuum solutions in the presence of a cosmological constant A from the point of view of dynamical system theory. Assuming a Friedmann-Robertson-Walker metric we plot the phase diagrams corresponding to all values of. The analysis of the diagrams allows us to determine several physical properties of the solutions as well as their global dynamical behaviour.     

General vacuum solution for Brans-Dicke-Bianchi type V

In this paper we have obtained the general vacuum solution for Bianchi type V in the Brans-Dicke theory. It is shown that for the special case=0, the sourceless scalar field is dynamically an essential factor which determines the cosmological expansion parametersR _i and the singularity does not occur whent=0. For this solution there is no antigravity (>0), which disagrees with other solutionsa for BDT-Bianchi type V     

Nonsingular cosmological models in Brans-Dicke theory

An attempt has been made to construct nonsingular cosmological models in Brans-Dicke theory by taking vacuum field as the long-range interacting scalar field which tends to avert the occurrence of initial singularity in a homogeneous and isotropic cosmological model. Such a model will possess an extremely small value of coupling parameter , as such they will be characteristically different from the usual Brans-Dicke models with 6. A justification for the estimated value of coupling parameter in the present paper has been given with particular reference to the helium problem. The model satisfies the initial conditions as proposed by Salam, Sinha, etc. However, it predicts a larger value of the energy density at the present epoch.     

A Crucial Ingredient of Inflation

Nonminimal coupling of the inflaton field to the Ricci curvature of spacetime is generally unavoidable, and the paradigm of inflation should be generalized by including the corresponding term R²/2 in the Lagrangian of the inflationary theory. This paper reports on the status of the programme of generalizing inflation. First, the problem of finding the correct value (or set of values) of the coupling constant is analyzed; the result has important consequences for the success or failure of inflationary scenarios. Then, the slow-roll approximation to generalized inflation is studied. Both the unperturbed inflating universe models and scalar/tensor perturbations are discussed, and open problems are pointed out.     

Causality in Inflationary Universes with Positive Spatial Curvature

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of , 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.     

Trapping the Kaluza-Klein scalar

The Kaluza-Klein unified theory predicts the existence of a Brans-Dicke type scalar field with = 0. Solar system experiments do, however, imply that gravitational scalar fields must be suppressed either by a very weak coupling to matter ( > 500) or a self-interaction. Here the consequences of a self-interaction potential of the Kaluza-Klein scalar are investigated. By suppressing the scalar field in this way, the one-body metric reduces to the Schwarzschild solution. The cosmologies of the scalar-tensor model are, however, very different from cosmologies of Einstein's theory, since here the time evolution of the cosmic scale-factor is determined only by the initial conditions. These may be chosen so that the theory is compatible with the hypothesis of primordial nucleosynthesis.