Conformally flat static space-time in the general scalar-tensor theory of gravitation

Explicit vacuum field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of the most general conformally flat spherically-symmetric static space-time. It is shown that the most general conformally flat spherically-symmetric static solution of Nordtvedt-Barker vacuum field equations is simply the empty flat space-time of general relativity.     

Black hole solutions in warped DGP brane world

Using the effective gravitational field equations in the warped DGP brane-world scenario (Maeda et al. in Phys. Rev. D 68:024033, 2003), we study spherically symmetric vacuum (static black hole) solutions on the brane. Working with a conformally flat bulk, we have obtained an exact Schwarzschild–de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant, which confirms the idea that an extra term in the effective vacuum field equations on the warped DGP brane can play the role of a positive cosmological constant.     

Exact Bianchi type-VI0 vacuum cosmological model in Brans-Dicke theory

We present an exact solution of the vacuum Brans-Dicke field equations for cosmological models of Bianchi type-VI₀. The solution represents anisotropic universe which has no analogy in Einstein's theory.     

Bianchi type I vacuum,field in Brans-Dicke theory

An exact solution of the vacuum Brans-Dicke field equations is obtained for the metric tensor of a spatially-homogeneous and anisotropic Bianchi type I configuration. The solution has no analogy in Einstein's theory for the layer values of the BD parameter. Some properties of the solution are discussed.     

Vacuum friedmann model in self-creation cosmology

The field equations of the self-creation theory of gravitation proposed by Barber are solved for a vacuum with the aid of a space-time metric of Friedmann. Some physical properties of the solution are discussed.     

Brans-dicke cosmology and the cosmological constant: The spectrum of vacuum solutions

We study the Brans-Dicke vacuum field equations in the presence of a cosmological term A. Considering a Friedmann-Robertson-Walker metric with flat spatial sections (k=0), we provide a qualitative analysis of the solutions and investigate its asymptotic properties. The general solution of the field equations for arbitrary values ofw and A is obtained.Work supported by CNPq (Brazil).     

Plane symmetric vacuum bianchi type I cosmological model in Brans-Dicke theory

The paper presents an exact solution of the vacuum Brans-Dicke field equations for the metric tensor of a spatially homogeneous and anisotropic cosmological model. The Kasner metric is shown as a special case. Some physical properties of the model are discussed.     

Cosmological electrovac model in Bertotti-Robinson space-time

Cosmological electrovac field equations are studied in Bertotti-Robinson-type space-time, and a class of cosmological solutions is obtained. The nature of the electromagnetic fields and singularities of the solution is studied. A technique is established to generate these solutions from a known vacuum solution with a non-zero cosmological constant.     

Comment on the Brans-Dicke-Bianchi type-I solution

We should like to point out that the Brans-Dicke-Bianchi type-I vacuum solution recently given by Ram and Singh is wrong. The correct solution is nothing but a special case of the general BDT-Bianchi type-I solutions given by us recently (Lorenz-Petzold, 1984). It is the aim of this comment to rediscuss the corresponding field equations and to disprove the statement that the (correct) solution has no analogy in Einstein's theory.     

Plane-symmetric vacuum in self-creation cosmology

Vacuum field equations for the static and non-static plane-symmetric metric are obtained in self-creation theory of gravitation proposed by Barber (1982). It is shown that, in both static and non-static cases, the only plane-symmetric solution in vacuum is the empty flat space-time of Einstein's theory. It is observed that this result is quite different from that of the Brans-Dicke and other scalar-tensor theories of gravitation.     

Thermodynamics of the universe filled with perfect fluid having variable equation of state

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Hor̃ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein’s general relativity at large distances. Subsequently Lü et al. have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences have been analyzed. Also the thermodynamics of the FRW universe has been studied.     

BIANCHI-I-Kosmen der BRANS-DICKE-Theorie für das Vakuum

The field equations of the BRANS -DICKE theory are solved for a vacuum with the aid of a space-time metric of BIANCHI -I-type. Two solutions are found. One of them corresponds to a generalization of the flat de SITTER -universe. On the other side we have obtained the KASNER -like solution on the basis of original the version of BRANS -DICKE theory.     

Exact Brans-Dicke-Bianchi type-VIIh solutions

We discuss the Brans-Dicke-Bianchi type-VII_h field equations. Exact solutions are given for the vacuum case as well as for the stiff matter case. The derived solutions are the generalizations of the GRT-solutions first given by Doroshkevichet al. (1973) and Lukash (1974a). In addition we present a new BDT-stiff matter solution which has no analogy in the GRT.     

Elliptic-type motion in Fock's gravitational field

The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined.     

Interaction of Gravitational field and Brans-Dicke field in R/W universe containing Dark Energy like fluid

On studying some new models of Robertson-Walker universes with a Brans-Dicke scalar field, it is found that most of these universes contain a dark energy like fluid which confirms the present scenario of the expansion of the universe. In one of the cases, the exact solution of the field equations gives a universe with a false vacuum, while in another it reduces to that of dust distribution in the Brans-Dicke cosmology when the cosmological constant is not in the picture. In one particular model it is found that the universe may undergo a Big Rip in the future, and thus it will be very interesting to investigate such models further.     

Five dimensional cosmological models in Lyra geometry with time dependent displacement field

In this paper exact solutions of the five-dimensional vacuum cosmological field equations based on Lyra geometry are obtained. Further it is shown that neither dust distribution nor perfect fluid distributions survive for the model. Some properties of the vacuum model are also discussed.     

On the scalar-tensor theory of Lau and Prokhovnik

Recently Lau & Prokhovnik (1986) have formulated a new scalar-tensor theory of gravitation which reconciles Dirac’s large numbers hypothesis with Einstein’s theory of general relativity. The present work points out an error in the time-dependent cosmological term and the scalar potential given by Lau and Prokhovnik. The correct forms for these quantities are derived. Further, a vacuum Robertson-Walker solution to the generalized field equations is obtained, under an anasatz that we propose, which illustrates that the theory is, in some sense, incomplete.     

A note on vacuum solutions based on Lyra's manifold

In a recent Letter to the Editor, Beesham (1986) has claimed that the models based on the Lyra manifold allow a wider class of solutions of the vacuum field equations than models based on a Riemannian manifold. It was also argued that the cosmological term is introduced in an arbitraryad hoc fashion in general relativity.In this note I will show that all the vacuum solutions found by Beesham, can equally well be solutions of the Friedmann equations of vacuum with a cosmological term. All these solutions are well known.     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Exact-Brans-Dicke-Friedmann-Robertson-Walker-Bianchi-Kantowski-Sachs vacuum solutions

Using a new method of reduction of the Brans-Dicke vacuum field equations we derive exact vacuum solutions for the class of spatially homogeneous space-times in a unified manner. Exact solutions are given for the isotropic Friedmann-Robertson-Walker models as well as for the anisotropic Bianchi types I-IX and for the related Kantowski-Sachs model.