Extended translational invariance and the tetrad theory of gravitation

A tetrad theory of gravitation is derived systematically from the requirement of localization of the group of translations. It is shown that when the sources of the gravitational field are chosen in the form of the total canonical energymomentum tensor of the nongravitating matter this gauge theory is identical with the previously formulated tetrad theory of gravitation in a space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 137–141, April, 1977.     

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.     

Polarization of vacuum of quantum fields in the Aaronov-Bohm external field. II

A spinor field interacting with the Aaronov-Bohm external field is examined. Analytical expressions for the vacuum average components of the energy-momentum tensor are derived. Dependences of the components of energymomentum tensor of the spinor field in the vacuum state on the distance and field strength are investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–8, April, 2006.     

Minimal and nonminimal gravitational interactions,and the asymmetric energy momentum tensor

Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b _k , which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincaré gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.An abridged version of the present paper was presented at the 6th International Conference on Gravitation and Relativity at Copenhagen, July 1972.Y. Nishina Memorial Foundation Fellow, on leave of absence from the University of Tokyo, Japan.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

含物质纯重力场部分贡献的静态和稳态重力场研究

给出了包含重力场贡献在内具有宇宙因子项最普遍形式的重力场方程为Rμν-gμνR/2+λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)/c4，这里λ为Einstein宇宙常数，Ｔ（Ⅰ）μν，Ｔ（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.物质纯重力场部分的能量-动量张量表述为T(Ⅱ)μν=(DμρＤρν-gμνＤαβＤαβ/4)/4πG，式中Dμν的定义为Ｄμν＝ωμ／xν-ων／xμ，ωμ≡-c2gμ0/g00.并用重力场贡献在内最普遍形式的重力场方程分别研究了几个大家所熟悉的静态和稳态重力场，像带有Einstein宇宙因子λ项球对称纯物质球外部静态度规、静态荷电球外部度规、匀速转动星体外部度规及理想纯物质星体内部静态平衡等,并进行了讨论. 关键词： 能量动量张量 重力场方程 静态重力场 稳态重力场     

Deflection in higher-order gravitational lensing

The deflection of light rays by rotating gravitational lens is considered in the framework of higher-order gravitational theory. The bending angle of light is derived. The effect of the massive scalar and tensor components of higher-order gravitational field as well as the gravito-magnetic on light deflection are discussed.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

The meaning of general covariance of einstein’s theory of gravity

The fundamental symmetry of Einstein’s theory of gravity is Lorentz-invariance which leads to a well defined energy-momentum tensor. This is also true for Maxwell’s theory of electromagnetism which has an additional symmetry due to its spin one, restmass zero character. Similarly, the spin two, restmass zero character of the gravitational field leads to an additional gauge symmetry that happens to be isomorphic to the concept of general covariance. The gauge-covariant energy-momentum tensor for gravitational interactions vanishes identically.     

Geometrical description of field algebra

The algebraic presentation, of the curvature tensor suggested earlier in [1] yields a simple form of the energymomentum tensor, presupposed by the Sugawara model. This expression gives rise to the expression of the Yang-Mills fields in terms of tetrads. This provides for an interpretation of the Yang-Mills fields as classical counter-parts of inhomogeneous group generators. A generalized form for the Yang-Mills fields is obtained for which commutation relations of the field algebra follow naturally.     

On the Rainich geometrization of a vector meson field in the Kibble theory

The variables of a vector meson field are determined within the framework of the Kibble theory as the functions of the metric tensor, affine connection and their derivatives and a system of differential equations is found for the metric tensor and affine connection which is equivalent to the equations of motion of gravitational and vector meson fields.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Limits of applicability of Gupta's theory

The applicability of the quantum theory of a weak gravitational field (Gupta's theory) is examined on the basis of the quasiclassical generally relativistic point of view. It is shown that in standard quantum theory the energy of a particle cannot be arbitrary but is bounded both below and above. These bounds arise because it is impossible to treat the region of interaction of elementary particles as a part of flat space. The lower limit depends on the curvature tensor of the external gravitational field, while the upper is determined by the gravitational field of the particle itself.     

A minimal relativistic model of gravitation within standard restrictions of the Classical Theory of Fields

The minimal relativistic model of gravitation on the basis of the gauge-invariant theory of the linear scalar massless field is suggested. The principle of the multiplicative inclusion of gravitational interaction, the requirements being that the simplicity and invariance of the theory under the allowed (gauge) transformation of potential Ф → Ф′ = Ф + const as the basis of the approach, is used. A system of gauge-invariant gravitational field and matter equations is obtained and an energy-momentum tensor with a positively defined density of the field energy is constructed. The exact solutions to equations for the central static field and for fields of spherically symmetric and plane gravitational waves in the free space and in the material media are obtained.     

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of(N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity(TEGR).The fundamental gravitational field variables are the(N+1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution(Schwarzschild(4+1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.     

Lorentz-Covariant theory of gravitation

A Lorentz-covariant theory of gravitation is proposed. It is based on a simple form of the Lagrangian for the gravitational field. The field equations have a simple mathematical structure where the energy-momentum tensor of matter and of gravitational field is the source of the field. The theory agrees with general relativity for the three well-known effects, i.e., red shift, deflection of light, and perihelion.     

On Thermodynamics of Kerr Black Hole

The gravitational Stefan–Boltzmann law is considered for the Kerr black hole in the weak-field limit. The energy-momentum tensor predicted by teleparallelism equivalent to general relativity is used in the thermo field dynamics formalism to thermalize the field. A temperature-dependent gravitational pressure is obtained. Regions of divergent heat capacity are observed. According to Landau theory, it allows the existence of distinct phases around the Kerr black hole.     

Nonlinear gravito-electromagnetism

There is a non-linear and covariant electromagnetic analogy for gravity, in which the full Bianchi identities are Maxwell-type equations for the free gravitational field, encoded in the Weyl tensor. This tensor gravito-electromagnetism is based on a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, and includes all non-linear effects from the gravitational field and matter sources. The non-linear vacuum Bianchi equations are invariant under spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. The super-energy density and super-Poynting vector of the gravitational field are natural duality invariants, and satisfy a super-energy conservation equation.