Bianchi Type-V Cosmological Model with Linear Equation of State in Brans-Dicke Theory of Gravitation

A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field øand scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

Improved routing strategy based on gravitational field theory

Routing and path selection are crucial for many communication and logistic applications. We study the interaction between nodes and packets and establish a simple model for describing the attraction of the node to the packet in transmission process by using the gravitational field theory, considering the real and potential congestion of the nodes. On the basis of this model, we propose a gravitational field routing strategy that considers the attractions of all of the nodes on the travel path to the packet. In order to illustrate the efficiency of proposed routing algorithm, we introduce the order parameter to measure the throughput of the network by the critical value of phase transition from a free flow phase to a congested phase,and study the distribution of betweenness centrality and traffic jam. Simulations show that, compared with the shortest path routing strategy, the gravitational field routing strategy considerably enhances the throughput of the network and balances the traffic load, and nearly all of the nodes are used efficiently.

The Gravitational Potential and the Gravitational Force According to the Correct Schwarzschild Metric

In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. In this article, by starting from this correct Schwarzschild metric, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Moreover, we analyse these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.

Bianchi type I in f(T) gravitational theories

A tetrad field that is homogeneous and anisotropic which contains two unknown functions A（t） and B（t） of cosmic time is applied to the field equations of f（T）, where T is the torsion scalar, T = T~μ_（νρ）S_μ^（νρ）. We calculate the equation of continuity and rewrite it as a product of two brackets, the first is a function of f（T） and the second is a function of the two unknowns A（t） and B（t）. We use two different relations between the two unknown functions A（t） and B（t） in the second bracket to solve it. Both of these relations give constant scalar torsion and solutions coincide with the de Sitter one. So,another assumption related to the contents of the matter fields is postulated. This assumption enables us to drive a solution with a non-constant value of the scalar torsion and a form of f（T） which represents ΛCDM.

THEORY OF GRAVITATIONAL RADIATION OF THE(Ω,A_μr)-FIELD

Further exploration of the fteld theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed 'The field Theory'.

Time evolution of the matter content of the expanding universe in the framework of Brans-Dicke gravity

A cosmological model has been constructed in the framework of Brans-Dicke(BD) gravity,based on an inter-conversion between matter and dark energy, for a spatially flat universe in the era of pressureless dust. To account for the non-conservation of the matter content, a function of time f(t) has been arbitrarily put into the expression for the density of matter(ρa^3= f(t)ρ_0 a_0~3). By definition, f(t) is proportional to the matter content of the universe. Using suitable ansatzes for the scale factor and scalar field, the functional form of f(t) has been determined from the BD field equations. The scale factor has been so chosen that it would cause a signature flip in the deceleration parameter with time. The function f(t) decreases monotonically with time, indicating a transformation of matter into dark energy. The time dependence of the proportions of matter and dark energy in the universe has been determined. The effect of non-conservation of the matter content upon various cosmological parameters has been explored in the present study. Two models of matter-energy interaction have been proposed and f(t) has been expressed as a function of their interaction term. The dark energy equation-of-state(EoS) parameter has been expressed and analyzed in terms of f(t).

Classical Theory of Advance of Perihelion of Mercury with Velocity Dependent Inertial and Gravitational Masses

It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.

A Possible Interpretation on Distance-Dependent Effect of Gravitational Constant in Newton＇s Theory of Gravitation

Based on the new metric theory of gravitation suggested by the author of this article, it gives a possible theoretical interpretation on the famous experiment done by D.R. Long in 1976, i.e. the distance-dependent effect of the gravitational constant in Newton's theory of gravitation.

A NEW MODELLING METHOD FOR EVALUATING EXTERNAL DISTURBING POTENTIAL BASED ON THEORY OF UNIFIED REPRESENTATION OF GRAVITATIONAL FIELD

For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.

Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.

Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry

We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models,the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior.Compared with the result of the standard ACDM model, the consequence suggests that the coupling between matter and geometry should be weak.

String cosmological models in the Brans-Dicke theory for five-dimensional space-time

Five-dimensional space-time string cosmological models generated by a cloud of strings with particles attached to them are studied in the Brans-Dicke theory. We obtain two types of interesting models by taking up the cases of geometric strings （or Nambu strings） and p-strings （Takabayasi strings）, and study their different physi- cal and dynamical properties. The roles of the scalar field in getting different phases, such as the inflationary phase and the string-dominated phase, are discussed. An in- teresting feature obtained here is that in one of the models there is a ＂bounce＂ at a particular instant of its evolution.

求Brans-Dicke理论中宇宙学解的一种简便方法

本文给出了一种比较简便的方法来处理标量一张量引力理论中 Brans-Dicke 场方程宇宙学模型的求解问题。利用这种方法,原先求解方法中必需分别处理的一个积分常数的三种不同值的情况,现在可以统一处理,并且得到的宇宙学解也可以表示为统一的形式。

五维Brans-Dicke引力理论的宇宙膨胀

将Brans -Dicke(BD)引力理论扩展到五维Kaluza -Klein时空 ,在物质场和BD标量场是空间均匀分布的假设条件下 ,提出五维时空的Robertson -Walker度规 ,由五维BD标 -张量引力场方程出发 ,导出宇宙动力学方程 ,建立以五维BD引力理论为基础的宇宙模型 ,求得标度因子为时间t的幂函数形式的宇宙膨胀解 。

Precise Measurements of the Gravitational Constant: Revaluation by the Information Approach

The gravitational constant discovered by Newton is still measured with a relative uncertainty that is several orders of magnitude larger than the relative uncertainty of other fundamental constants. Numerous methods are used to measure it. This article discusses the information-oriented approach for analyzing the achievable relative measurement uncertainty, in which the magnitude of the gravitational constant can be considered as plausible. A comparison is made and the advantages and disadvantages of various methods are discussed in terms of the possibility of achieving higher accuracy using a new metric called comparative uncertainty, which was proposed by Brillouin.

Brans-Dicke理论和f(R)理论中的可穿越虫洞

Brans-Dicke理论和f(R)理论均为不同于Einstein广义相对论的修正引力理论,并且在Brans-Dicke理论参数ω=0时能够回到f(R)理论.人们在Brans-Dicke理论框架下研究得出只有-3/2<ω<-4/3才存在可穿越虫洞,ω=0时没有;然而,f(R)理论中已经证明确实也存在可穿越虫洞.为了解决上述所谓的矛盾,有文献修改了Brans-Dicke理论中的某些函数,从而改变ω的取值范围.仔细分析发现,文献中探讨的是对应不同Φ(r),b(r)的可穿越虫洞,自然会给出不一致的结论.本文对2种修正引力理论中的可穿越虫洞问题进行了澄清,明确了各自虫洞解的讨论前提条件.

QED-Like Simple High Order Perturbative Relation between the Gravitational Constant <i>G</i>and the Planck Constant <i>h</i>

We find a simple precise formula for the gravitational constant G relating it to the electron charge, electron mass, the vacuum dielectric constant and the speed of light (or magnetic permeability of the vacuum) in power of the fine structure constant i.e. relating the gravitational constant to the Planck constant through others which also well exist without the quantum mechanics therefore relating two fundamental constants as not independent through the parameters of the electron and the electromagnetic properties of the vacuum.

Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.

A note on teleparallel Killing vector fields in Bianchi type Ⅷ and Ⅸ space-times in teleparallel theory of gravitation

In this paper we classify Bianchi type Ⅷ and IX space-times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type Ⅷ and Ⅸ space-times in the context of teleparallel theory are different from that in general relativity.

Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dμ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A^α μ （x） have spherical symmetry, depending only on the radial coordinate τ is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.