On Treder-Type Tetrad Theories of Gravitation II. Treder's Tetrad Theories in Linear Approximation

We consider some properties of TREDER'S tetrad theories, derived in I, using the field equations proposed by KASPER and LIEBSCHER . The linearized theory is considered, because the field energy becomes positive, if the energy of the weak field is a positive one. Using the dynamical equations, the field equations lead for the symmetric part of the field to the gauge invariant field equations in Hilbert gauge and to corresponding equations for the antisymmetric part. This means that in this approximation the dynamical equations replace the gauge invariance and the tetrad field corresponds to a mixture of tensor and scalar gravitons. We discuss possible experiments for showing the existence of scalar gravitons and limiting the free parameter of the theory.     

Regular Charged Solutions in Mφller＇s Tetrad Theory of Gravitation

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenbock spacetime.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.     

On Treder-Type Tetrad Theories of Gravitation I. Equivalence Principle and Invariance Properties

The Principle of relativity and the equivalence principle are the most important foundation of any theory of gravitation. We can formulate these principles by the help of the LORENTZ and the EINSTEIN groups. If we start with an action functional, the demand of invariance of this action with respect to these groups makes possible to get detailed conclusions about the general structure of theories of gravitation. EINSTEIN'S idea, to interpret gravitation as deformation of the local inertial systems of the special theory of relativity, leads to bi-tetrad theories, which we call TREDER-type tetrad theories. In this theories a sufficient number of gauge parameters is introduced in order to ensure the invariance of the action functional without limitations for the field variables.     

A Dark Energy Model in a Scale Covariant Theory of Gravitation

An axially symmetric Bianchi type-I space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-V Dark Energy Model in a Scalar-Tensor Theory of Gravitation

A spatially homogeneous and anisotropic Bianchi type-V universe with variable equation of state (EoS) parameter and constant deceleration parameter is obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). The physical and kinematical properties of the universe have been discussed.     

Bianchi Type-II Dark Energy Model in Scale Covariant Theory of Gravitation

Spatially Homogeneous and anisotropic Bianchi type-II space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

The Vaidia Equations in the Bruns-Dicke-Jordan Gravitation Theory

The equations of the scalar-tensor Bruns-Dicke-Jordan gravitation theory are studied. The field equations are rearranged into a Vaidia form by means of conformal transformation (the right-hand side of the equations has the form of the Vaidia energy-momentum tensor for radiation) depending on the scalar field. The compatibility equations for the scalar field are found in the general case for the field relations obtained. An example of solution to these equations for homogeneous spaces is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 43–46, May, 2005.     

LRS Bianchi Type-I Dark Energy Cosmological Model in Brans-Dicke Theory of Gravitation

Bianchi type-I dark energy model with variable equation of state (EoS) parameter is presented in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To get a determinate solution of the field equations we will take the help of special law of variation for Hubble’s parameter presented by Bermann (Nuovo Cimento B. 74:182, 1983) which yields a dark energy cosmological model with negative constant deceleration parameter. It is observed that this dark energy cosmological model always represents an accelerated and expanding universe and also consistent with the recent observations of type-Ia supernovae. Some physical and geometrical properties of the model are also discussed.     

Two Fluid Scenario for Dark Energy Model in a Scalar-Tensor Theory of Gravitation

In this paper, we investigate the evolution of dark energy parameter in the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy in the framework of scalar-tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A 113:467, 1986). To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:183, 1983) is used. We consider the two cases of interacting and non-interacting fluid (barotropic and dark energy) scenario and obtained general results. The physical aspects of the results obtained are also discussed.     

Axially Symmetric Cosmological Model with Wet Dark Fluid in Bimetric Theory of Gravitation

The purpose of this paper is to investigate the role of wet dark fluid in axially symmetric cosmological model within the frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). In this theory, it is observed that there is no contribution from wet dark fluid.     

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

万有引力理论的实验检验

牛顿(1642～1727)发现万有引力定律的曲折历程和传奇故事多见于教学参考资料,但对于牛顿发现万有引力定律到世人公认定律的一段曲折历史却少见叙述,笔者查阅了有关文献,特撰文对此作一个补遗.……     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

A Non-geometric Relativistic Theory of Gravitation

A non-geometric relativistic theory of gravitation is developed by defining a semi-metric to replace the metric tensor as gravitational vector potential. The theory show that the energy-momentum tensor of the gravitational field belong to the gravitational source, gravitational radiation is contained in Einstein’s field equations that including the contribution of gravitational field, the real physical singularity in the gravitational field can be eliminated, and the dark matter in the universe is interpreted as the matter of pure gravitational field.     

A Cosmological Model with Negative Constant Deceleration Parameter in a General Scalar-Tensor Theory of Gravitation

Spatially homogeneous and anisotropic LRS Bianchi type-I metric is considered in the framework of Nordtvedt-Barker’s general scalar-tensor theory of gravitation when the source for the energy momentum tensor is a perfect fluid. With the help of a special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cim. B. 74:182, 1983) a cosmological model with negative constant deceleration parameter is obtained. Some physical and kinematical properties of the model are also discussed.