Algebraic classification of gravitational fields in five-dimensional space-time

We consider the algebraic classification of five-dimensional empty space-time (Kalutsa type) with one time-like direction as a generalization of the Petrov algebraic classification of gravitational fields in four-dimensional space-time. We study two special cases: a) zero electromagnetic field and zero scalar field; b) nonzero electromagnetic field and zero scalar field. For the (1+4) separated Kalutsa five-metric we introduce the pentad metric of a tangent five-space, which is mapped together with the curvature tensor into a ten-dimensional real flat vector space. The classification is constructed in local geodesic coordinates for the above two cases. In both cases the characteristic equation can be reduced to a sixth-order equation that can be simplified when certain requirements are satisfied. Our results demonstrate the nontrivial nature of algebraic classification in five dimensions.This work was performed within the framework of the State Science and Technology Astronomy program.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 73–78, March, 1995.     

On the theory of inertial gravitational fields

The generalized equations of the inertial gravitational field are derived from variational principles. It is shown that variational properties of inertial gravitational potentials have important peculiarities which cause peculiarities of equations obtained.     

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory.     

Republication of: Quantum theory of weak gravitational fields

This is an English translation of a paper by Matvei Bronstein, first published in German in 1936 in a long-extinct Soviet journal, in which he presented the first attempt at quantizing a weak (linearized) gravitational field, rather modern in its approach. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Stanley Deser and Alexei Starobinsky, and Bronstein’s brief biography written by Stanley Deser.     

Hamiltonian formulation of the theory of interacting gravitational and electron fields

The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x^o = constant hyper-surfaces (“time gauge”) the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent.     

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     

Twistor theory: An approach to the quantisation of fields and space-time

Twistor theory offers a new approach, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. Twistors for flat space-time are the SU(2,2) spinors of the twofold covering group O(2,4) of the conformal group. They describe the momentum and angular momentum structre of zero-rest-mass particles. Space-time points arise as secondary concepts corresponding to linear sets in twistor space. They, rather than the null cones, should become “smeared out” on passage to a quantised gravitational theory. Twistors are represented here in two-component spinor terms. Zero-rest-mass fields are described by holomorphic functions on twistor space, on which there is a natural canonical structure leading to a natural choice of canonical quantum operators. The generalisation to curved space can be accomplished in three ways; i) local twistors, a conformally invariant calculus, ii) global twistors, and iii) asymptotic twistors which provide the framework for an S-matrix approach in asymptotically flat space-times. A Hamiltonian scattering theory of global twistors is used to calculate scattering cross-sections. This leads to twistor analogues of Feynman graphs for the treatment of massless quantum electrodynamics. The recent development of methods for dealing with massive (conformal symmetry breaking) sources and fields is briefly reviewed.     

Absorption of gravitational waves by an excited vacuum space-time

We discuss modifications of Einstein's equations generated by vacuum fluctuations of the gravitational field. A special case of excitation is shown to be responsible by absorption of gravitational waves.     

Some properties of the gravitational fields of a hydrodynamical fluid and dust

Conditions are obtained on the four velocity of the particles of a medium in the gravitational fields of a hydrodynamical fluid and dust, and the nature of the motion of the medium in these fields is investigated. It is shown that the gravitational fields of a hydrodynamical fluid and dust do not admit conformal mapping onto Einstein spaces which are not conformally flat spaces (spaces of constant curvature).     

Matter fields in the Plebanski-Demianski space-time

We consider the boson (electromagnetic and gravitational) fields and the fermion (electron and neutrino) fields in the Plebanski-Demianski space-time. In the case of the boson field, we observe that the superradiance phenomena occurs, but in the case of the fermion field we find no super-radiance phenomena     

Homogeneous and isotropic solutions of a gravitational theory with scalar fields

We study the homogeneous and isotropic solutions of a gravitational theory with scalar fields. Qualitative characteristics of these solutions are analyzed and important differences with respect to the usual Einstein theory are pointed out.     

Five-dimensional theory of interacting scalar,electromagnetic, and gravitational fields

An (n+1) factorization of an (n+1)-dimensional Riemann manifold is performed. For a space permitting a Killing vector, the (n+l)-dimensional Hubert variational principle reduces to the variational principle for the corresponding quantities in an n-dimensional space. Hence, setting n=4 and n=3, versions of a unified theory of gravitational, electromagnetic, and scalar fields and the steady-space theory of general relativity theory, respectively, are constructed. The five-dimensional variational principle for geodesics reduces to the four-dimensional leastaction principle for the test charged particle moving in gravitational, electromagnetic, and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 58–65, November, 1979.     

Foundations of the unified theory of gravitational,electromagnetic, and scalar fields

A particular case of bimetrical unified field theory is considered, which is based on Hilbert's proposal of obtaining a complete system of independent equations for unified theory. The action depends on two symmetrical tensors g_μν and g _μν ^° , the second leading to a zero curvature tensor, which results in the theory being invariant under the Poincaré group, and in ten conservation laws. The field equations obtained when varying the action with respect to g_μν have the form of Einstein equations whose righthand side is not defined independently, but is rather a function of g_μν and g _μν ^° . The vector and scalar gauge transformations corresponding to variations δS of special form are defined. With the aid of these transformations, the electromagnetic and scalar fields are introduced within the framework of the unified theory. The basic equations of the theory under consideration contain a new dimensional physical constant, which connects gravitation and electromagnetism. A numerical estimate of this constant is given.     

Creation of particles by time-dependent gravitational fields

A method based on the formulation of a quantum equivalence principle is introduced in order to define particle annihilation and creation operators during the expansion of the universe. Our theory predicts the creation of a finite number of particles.     

Null surface quantization and quantum theory of massless fields in asymptotically flat space-time

The quantum theory of massless fields in an asymptotically simple space-time is developed. The Schwinger dynamical principle and the Penrose conformal technique are exploited to derive the commutation relations on proper null surfaces in a curved space-time and on null infinities. The explicit expression for theS matrix in an asymptotically simple space-time is presented. The general expression for a density matrix describing particles created in an external field is also given and its possible applications are discussed briefly.     

Non-linear quark theory of spin 2 fields (gravitational mesons). II

An equation for spin 1/2⁺ and 3/2⁺ fermions interacting with a 27-plet of gravitational mesons is derived by the confluence method in the framework of non-linear quark theory of elementary particles. The case of spin 1/2⁺ baryons is examined in detail, and the equation for the baryon octet is derived in the form of an equation for a spinor field in curved space (the Fok-Ivanenko equation). An effective metric is defined by means of the 27-plet of gravitational mesons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 7–11, April, 1973.     

On the models of gravitational fields

Modelling of the gravitational field is discussed within the framework of Einstein's theory. Modelling is defined as the mapping whereby the geodesic lines (the path of test bodies) go into the family of curves given by the equation of a test body motion in a model. Different possible ways of modelling are singled out — namely, the complete, selective, and approximate-selective ones. The theory is applied to the solar gravitational field.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971. Professor Petrov died in the Summer of 1972. He was one of the members of the International Committee on GRG and founder of the Journal on GRG. We are happy to publish this contribution of his and shall respectfully keep him in our memory. (The Editor.)     

A dilemma in the physics of gravitational fields

It is shown that improper use of local quantities for nonlocal situations in fields leads to traditional errors. Nonlocal theoretical quantities referred to standards in a fixed field are defined in order to obtain reliable results. Nonlocal properties of gravitational fields and matter located in it are deduced with the help of physical principles and an electromagnetic model for matter. In spite of the fact that the local velocity of light should be constant, the field is a space of variable nonlocal velocity of light, which accounts for its properties. Matter and light virtually propagate themselves without exchanging energy with the external field, in disagreement with traditional assumptions. Matter becomes contracted by the field. The results are self-consistent and consistent with the observed facts. Bodies withr2GM would be different from black holes and they may account for the peak of highest energy of cosmic radiation and other astronomical facts.