Nonlinear Spinor Field Equations in Gravitational Theory: Spherical Symmetric Soliton-Like Solutions

This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.

Riemannian Space-Time, de Donder Conditions and Gravitational Field in Flat Space-Time

Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.

Note on Energy-Momentum Tensor for General Mixed Tensor-Spinor Fields

This note provides an explicit proof of the equivalence of Belinfante's energy-momentum tensor and metric energy-momentum tensor for general mixed tensor-spinor fields.

Gravitational radiation fields in teleparallel equivalent of general relativity and their energies

We derive two new retarded solutions in the teleparallel theory equivalent to general relativity （TEGR）. One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitational energymomentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.

The Basic Concepts and Basic Laws Relating to Matter and Gravitational Fields in Physics

In this work, the author applied the universal gauge field theory and Noether theorem to prove that universality exists for the Lorentz and Levi-Civita law of conservation of energy momentum tensor density. We also found that this conservation law has profound implications in physics. For example, based on this law, one can explore the origin of the matter field, and propose a new view about what is “dark energy” and what is “dark matter”.

A Locally Conservative Energy-Momentum Tensor in the General Relativity Based on a Cosmological Model without Singularity

According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.

Curvature Energy and Their Spectrum in the Spinor-Twistor Framework: Torsion as Indicium of Gravitational Waves

The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that derive of mass-energy source in the space-time and whose contorted image is the spectrum of the torsion field acting in the space-time. The energy of this field is the energy of their second curvature. Likewise, it is assumed that the curvature energy as spectral curvature in the twistor kinematic frame is the curvature in twistor-spinor framework, which is the mean result of this work. This demonstrates the lawfulness of the torsion as the indicium of the gravitational waves in the space-time. A censorship to detect gravitational waves in the space-time is designed using the curvature energy.

Fourth Rank Energy-Momentum Tensor

In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

Representation of Physical Fields as Einstein Manifold

In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.

Forward Modeling of Gravity,Gravity Gradients,and Magnetic Anomalies due to Complex Bodies

On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.

Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory

We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). Equations with power and polynomial nonlinearities are studied in detail. In this case, a soliton-like configuration has negative energy. We have also obtained exact static plane-symmetric solutions to the above spinor field equations in flat space-time. It is proved that in this case soliton-like solutions are absent.

Time-Machine Solutions of Einstein's Equations with Electromagnetic Field

In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori＇s, we solve the Einstein＇s equations with the energy-momentum tensors for electromagnetic field, and construct the time-machine solutions, which solve the time machine problem in electromagnetic field.

On Quasi-Einstein Field Equation

In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.

The gravitational gradient tensor’s invariants and the related boundary conditions

Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O ( J 2/2 T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10-7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10-8 and the order can reach up to 280.

复杂形体重力场、梯度及磁场计算方法

在改进均匀多面体重力场正演公式基础上,利用二阶张量的坐标变换实现对多面体重力场梯度的求解,推导了新的多面体重力梯度和磁场的正演公式,给出了新的统一的均匀多面体重力场、梯度及磁场正演表达式形式,并用理论模型进行了检验.同时,应用新的多面体重力场梯度正演公式推导出新的长方体重力场垂直梯度理论表达式.本文给出的均匀多面体重力场、梯度及磁场正演表达式形式统一,重磁场联合正演中可相互利用其计算过程中的结果,避免重复计算以提高正演计算效率.

有挠引力场之能动张量密度及自旋密度的再研究

在有挠情况下对引力场的能动张量密度及自旋密度进行了再研究，肯定了定义Ｔ（Ｇ）μｉｄｅｆδＬＧ／δｈｉμ及Ｃ（Ｇ）μｉｊｄｅｆ－２δＬＧ／δΓｉｊμ的合理性，导出了引力波虽存在但不携带能量、动量及自旋的结论．

荷磁矩中子星外部的电磁场能量动量张量

利用王永久等人所得到的具有磁矩的球对称质量外部的引力场度规和电磁势的表达式,计算出了球对称质量外部的电磁场量动量张量。数值计算结果和分布曲线表明,时空的弯曲将引起磁偶极子电磁场能量的增加。

引力场的运动方程及引力波的互作用

在Ｖｉｅｒｂｅｉｎ表述的局域Ｌｏｒｅｎｔｚ群引力规范理论中，合理地定义了引力场的张力张量，给出了广义协变的引力场的运动方程，讨论了一般对角度规引力波情况以及Ｂｏｎｄｉ引力平面波、引力孤立波各部分之间的互作用等有关问题．

引力场能动张量定义的历史争论及重新研究

引力场的能动张量是引力理论中一个极为重要的物理量 .八十多年前 Levi-Civita等人同爱因斯坦曾就这个量的定义及守恒律展开过一次重大争论 .后来虽然爱因斯坦的观点占了上风 ,但其定义的引力场能动张量 ,由于缺乏协变性 ,成了至今尚未完满解决的“老大难”问题 .文章对这场争论的前因后果和双方的观点进行了较详细叙述 ;且结合作者自己的研究对这场争论作了新的评论 ;并介绍了作者重新研究的成果 ,特别是引力波不传播能量的新观点及可能的实验验证 .