Spin rotation by Earthʼs gravitational field in a “frozen-spin” ring

Detailed calculations of spin rotation by the Earth?s gravitational field in a frozen-spin ring are presented in three different coordinate systems and used (a) to show that the systematic error caused by gravitation in a proposed electric dipole moment measurement can be unambiguously determined, and (b) to propose measuring the spin-gravity effect in a dedicated frozen-spin ring using electrons.     

Variational formalism and field equations of tetrad gravitation theory in the Weyl-Cartan space

A variational formalism of tetrad gravitation theory is developed in the Weyl-Cartan space with independent variations in the tetrad coefficients, metric tensor components, and affine connectivity coefficients that considers the Weyl condition imposed on the nonmetricity based on the method of undetermined Lagrange multipliers. The gravitational field equations are derived for the Lagrangian comprising all possible quadratic convolutions of curvature, torsion, and nonmetricity tensors in addition to the linear component. Differential identities are obtained for the general gravitational Lagrangian in the Weyl-Cartan space. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 56–59, June, 2006.     

Field theoretic treatment of gravitational interaction in electrodynamics

A theory of gravitational interaction in classical electrodynamics is developed on the basis of an earlier-proposed minimal relativistic model of gravitation. From the variation principle, a system of gaugeinvariant equations of the interacting electromagnetic and gravitational fields is deduced and their common energy-momentum tensor is constructed. A rigorous solution to the problem of regularizing the field mass of a point charge is given with consideration for the coupling energy of the gravitational interaction. The propagation of electromagnetic waves in the gravitational field is discussed. It is shown that, under the condition of the existing resonant ratio 2: 3 for the periods of Mercury’s orbital revolution and daily rotation, tidal forces cause a regular shift in the planet’s perihelion in an observable forward direction.     

On limiting field strengths in gravitation

We consider through the equivalence principle the existence of maximal and minimal field strengths in gravitation. We explore the consequences for gravitational collapse and for explaining the rotation curve of galaxies without invoking dark matter. Other interesting implications like maximal size of planetary systems are outlined.1. Note that, in our case, such results, both for electromagnetic and gravitational fields, are obtained when torsion is considered [8]: In fact, we have arrived at a minimum radius, for instance, of the electron, starting explicitly frm a modified Poisson's equation when a term containing the spin is incorporated through torsion.     

Linearized Higher-Order Gravity and Stellar Structure

Starting with the general "quadratic gravity" in four dimensions, linearization, assumption of the weak gravitational field to be static and matter to be a perfect fluid, one arrives at the modified Lane-Emden equation. The solutions of the modified Lane-Emden equation are found and the formulas for the stellar radius are obtained in two cases of the polytropic index N = 0 and N = 1. The influence of the additional Yukawa forces in the linearized higher-order gravitation on the Newtonian stellar structure is discussed.     

Poincaré引力规范场和1/2自旋粒子的运动

木文以Poinaré群作为引力规范群,在有挠率和曲率的空间中,讨论了当引力拉氏量包含场强的线性项与二次项时体系的运动方程,指出球对称真空静引力场方程在“宏观”极限下可以得到Schwarzchild解,因此它与目前关于广义相对论的实验验证是一致的,但在“微观”极限下,方程预示着一种新的短程作用,讨论了自旋1/2的粒子作为检测粒子在这种球对称真空静场中的运动,指出运动方程只与仿射联络的黎曼部分有关,并和广义相对论的相应方程具有同样的形式。 关键词：     

Energy-Level Shifts of a One-Electron Atom in Higher-Derivative Gravitational Field Caused by High-Power Laser Pulse

The gravitational field produced by a high-power laser pulse traveling with a velocity < c is found in the framework of higher-derivative theory of gravitation. The gravitational perturbations of the energy levels of a freely falling one-electron atom in the higher-derivative gravitational field are studied. The energy-level shifts of highly excited hydrogen atom are considered, and the influence of the additional forces included in the linearized higher-derivative gravitation on the energe level shifts of the atom is investigated.     

关于矢量-张量引力相互作用模型

本文从粒子运动方程出发证明了矢量-张量引力模型中反引力的存在,这种反引力如果以长程力的形式出现,将使得粒子的运动偏离短程线。在牛顿近似和弱场近似下,相应于矢量场的反引力与相应于张量场的吸引力互相抵消,使得检验粒子在球对称静态引力场中的加速度为零,这显然与牛顿万有引力现象矛盾。 关键词：     

Generalised cosmological friedmann equations without gravitational singularity

Within the framework of the gauge approach to gravitation, including terms in the lagrangian quadratic in the curvature and torsion tensors, a generalised Friedman equation for a homogeneous isotropic cosmology is obtained. This equation avoids the gravitational singularity with infinite mass density.     

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.     

On calculation of magnetic-type gravitation and experiments

The linearized Einstein equations are written in the same form as the Maxwell equation. In the case of a weak stationary field and low velocity, the geodesic equations are written in the form of the Lorentz equation of motion. We suggest that the existence of the magnetic-type gravitation predicted by GR is equivalent to the existence of the gravitational wave predicted by GR. The Schiff effect is explained as one of the magnetic-type gravitation and the new effect is given. The Hall-type gravitational experiment is studied.     

On Sakharov's theory of gravitation

The Sakharov theory of gravitation is examined from the viewpoint of the analogy between gravitation and elasticity. It is found that, by using the Cattaneo-Zel'manov projection technique, the deformation tensor connected with the gravitational field can be considered the deformation tensor of a suitable elastic medium. By supposing that transversal waves propagate in this medium with velocityc, one can find an explicit expression for the time dependence of the gravitational constant. Some applications of cosmological interest are briefly discussed.     

On Gravitational Energy in Newtonian Theories

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton–Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.     

关于引力场的能量问题

本文讨论引力场中局部区域的能量问题。这里提出了一个新的引力场总能量-动量赝张量密度,它所表示的引力场局部空间区域中的能量对纯空间坐标变换是不变量,因而引力场的局部区域能量具有确定的物理意义。关于Schwarzschild场的能量和动量,新的赝张量给出的结果要比现有广义相对论文献中的其他形式的赝张量所给出的结果较为合理。文中还讨论了在引力理论中质量与能量的关系问题。 关键词：     

Precession of Orbiting Gyroscope in Higher-Order Gravitational Field Caused by Rotating Body

The metric for a spinning massive object with any shape and composition is found by the use of linearized higher-order theory of gravitation. The geodesic and the Lense–Thirring precessions for an orbiting gyroscope in a general weak higher-order gravitational field are considered. The influences of the additional Yukawa forces included in the linearized higher-order gravitation on the precessions are investigated.     

引力场中的应力张量及其应用

根据引力场和静电场的相似性质，通过类比方法由静电场的麦克斯韦应力张量得出了引力场中的应力张量，并用它计算均质球体内部的万有引力。     

The interaction of a quantum mechanical oscillator with gravitational radiation

Within the framework of the linearized field equations of gravitation, the interaction operators between a quantum mechanical system and an external gravitational field are derived from the general-covariant Klein-Gordon and Dirac equation. In the case of linearly polarized plane gravitational waves the transition probabilities for absorption and induced and spontaneous emission of gravitational radiation by a quantum mechanical harmonic oscillator are calculated with the help of the time-dependent perturbation method. The results coincide with the classical ones according to the correspondence principle.     

The field of a charge in the bimetric gravitation theory

The field equations of the bimetric theory of gravitation are solved for the static, spherically symmetric electric and gravitational fields due to a point charge, subject to certain restrictions.     

A Generally Covariant Wave Equation for Grand Unified Field Theory

A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group.     

A scalar field theory of gravitation

A scalar theory of gravitation is developed from a variational principle. The speed of light is taken to be a function of the potential of the gravitational field. The predictions of the light deflection and the advancement of the perihelion agree with those made by Einstein's theory. The gravitational (active) mass differs from the inertial (passive) mass and both are dependent on the gravitational potential.