Electrostatic induction in Einstein-Maxwell theory

We investigate the physics of an exact static solution representing a mass Q and a charged mass P. We find that the electric field has a neutral point, and we ascribe this to the effect of a pseudocharge induced on Q. The induced field is local in that it does not have inverse square strength at infinity.     

Gauge gravitation theory

The particularity of the gauge gravitation theory is that Dirac fermion fields possess only Lorentz exact symmetries. It follows that different tetrad gravitational fieldsh define nonisomorphic representations _h of cotangent vectors to a space-time manifoldX ⁴ by Dirac's-matrices on fermion fields. One needs these representations in order to construct the Dirac operator defined in terms of jet spaces. As a consequence, gravitational fieldsh fail to form an affine space modeled after any vector space of deviationsh'–h of some background fieldh. They therefore fail to be quantized in accordance with the familiar quantum field theory. At the same time, deformations of representation _h describe deviations ofh such thath + is not a gravitational field. These deviations form a vector space, i.e., satisfy the superposition principle. Their Lagrangian, however, differs from familiar Lagrangians of gravitation theory. For instance, it contains masslike terms.     

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.     

The center-of-mass in Einsteins theory of gravitation

We prove the existence and uniqueness of a center-of-mass line as well as a center-of-motion line, the latter due toG. Dixon, 1964. The validity of the theorems depends on some assumptions listed in § 2, whose most restrictive ones (in the sense of physics) state a certain weakness of the gravitational field. In the concluding paragraph we give some corrolaries and a very simple application to the problem of motion.Essentially this work has been done during the authors stay at the Seminar f. Allg. Relativitätstheorie, Univ. Hamburg.     

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (Sect. 4.1). For the standard test cases (PPN scheme, Schwarz schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.     

Spontaneous compactification in six-dimensional Einstein-Maxwell theory

A discrete set of solutions to the classical Einstein-Maxwell equations in six-dimensional space-time is considered. These solutions have the form of a product of four-dimensional constant curvature space-time with a 2-sphere. The Maxwell field has support on the 2-sphere where it represents a monopole of magnetic charge, n = ±1, ±2, …. The spectrum of massless and massive states is obtained for the special case of flat 4-space, and the solution is shown to be classically stable. The limiting case where the radius of the 2-sphere becomes small is considered and a dimensionally reduced effective lagrangian for the long range modes is derived. This turns out to be an SU(2) × U(1) gauge theory with chiral couplings.     

Higher-order theory of gravitation

The field equations obtained by introducing a correction in the Hubert Lagrangian in the form of a series of finite terms inR (g R ) are considered in order to study the implications for the cosmological singularity.     

Relativistic theory of gravitation

In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly filfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just flat. This suggests that in the universe a missing mass should exist in a form of matter.     

Generalized theory of gravitation

The mathematical formulation of the nonsymmetric gravitation theory (NGT) as a geometrical structure is developed in a higher-dimensional space. The reduction of the geometrical scheme to a dynamical theory of gravitation in four-dimensional space-time is investigated and the basic physical laws of the theory are reviewed in detail.     

The causality principle in relativistic gravitation theory

It is shown that relativistic gravitation theory is consistent with the existence of vacuum-like medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 20–25, April, 2007.     

Many-time hamiltonian gravitation theory

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

The cosmology of the nonsymmetric theory of gravitation

We show that during cosmological inflation the nonsymmetric metric tensor theory of gravitation develops a spectrum which is potentially observable by cosmic microwave background observations, and may be the most sensitive probe of the scale of cosmic inflation.     

Double-dual solutions of generalized theories of gravitation

Solutions to the Stephenson-Yang theory of gravity and its generalizations are discussed. By considering the inclusion of a cosmological term in the action spherically symmetric static solutions are presented that do not fall into the vacuum Einstein class. A simple double-duality ansatz is responsible for all the solutions that are discussed.On leave from the Physics Department, Middle East Technical University, Ankara, Turkey.     

Einstein-Maxwell theory in 2+1 dimensions

Einstein-Maxwell theory in 2+1 dimensions is considered as a toy model for the 3+1 theory and as a means for understanding field theories without a background space-time geometry. Two possible approaches to the quantization of this theory are presented, one based on a Schwinger-Tomonaga time evolution equation and the other on a loop space construction, and the problems arising in both of these are discussed.     

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.     

Rigid motions and generalized Newtonian gravitation

In an effort to contribute to a better understanding of General Relativity, here we lay the foundations of generalized Newtonian gravity, which unifies inertial forces and gravitational fields. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally, we prove that the theory we propose here can be obtained as the non-relativistic limit of General Relativity.     

A bi-metric theory of gravitation

A bi-metric theory of gravitation is proposed, satisfying the covariance and equivalence principles. It is based on a simple form of Lagrangian and has a simpler mathematical structure than that of the general theory of relativity. The theory agrees with general relativity up to the accuracy of the observations made up to now. The static spherically symmetric solution of the present field equations does not involve any 'black hole'.     

Space-time foliations in gravitation theory

A relationship is established between gravitational fields and space-time foliations on a manifold X⁴; the gravitational singularities are described as singularities of these foliations representing critical points of real functions on X⁴.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 20–23, September, 1982.     

On the Goldstonic gravitation theory

The physical specificity of gravity as a Goldstone-type field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supergravity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular “dislocation” structure of a space-time due to Poincaré translation gauge fields and the corresponding modification of Newton’s gravitational potential are predicted.