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.     

On Rosen's bi-metric theory of gravitation

The field equations of Rosen's bi-metric theory of gravitation [1] are solved exactly. The solutions are the same as in the author's theory of gravitation [2]. These solutions are, however, incompatible with Rosen's conservation laws and his second (flat) metric. Incompatibility with the conservation laws arises in second order. Incompatibility with the flat metric arises in first order but only for time-dependent fields. Rosen's theory is defensible only as a static first order theory and predicts the red shift light deflection and time-delay correctly.     

On the bimetric theory of gravitation

Rosen's bimetric theory is analyzed anew and is shown to have deficiencies if the space is assumed to be Riemannian. The problems are due mainly to the introduction of the flat metric , and the identification of the stress-energy tensor,T . It is indicated that if the Riemannian interpretation could be avoided the theory still holds promise as a viable theory of gravitation.     

On a new metric affine theory of gravitation

We present three hypotheses which underlie a new general relativistic theory of gravitation for microphysical systems. According to this theory the metric and the independent affine connection of spacetime are determined by the momentum current and the newly recognized “hypermomentum” current of matter.     

On the most general linear theory of gravitation

The most general field theory of gravitation is analyzed both group theoretically as well as physically. The field equations are solved by means of an algebraic method and it is found that any field theory of gravitation contains only one essential parameter which is correlated to the spin 0 content of the field. Further it turns out that any theory of gravitation must contain a nonvanishing spin 0 part, but general relativity is distinguished by the fact that its spin 0 component cannot be radiated.     

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.     

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.     

On the meaning of a non-renormalizable theory of gravitation

The renormalizability of quantum gravity remains an open question while it has been established recently that quantum gravity in the presence of standard sources is non-renormalizable. In view of traditional confusion and ambiguities surrounding non-renormalizable quantum field theories, it has been felt that physical theories must be renormalizable. Recently a new, nonperturbative view of non-renormalizable theories has been suggested that may have relevance for various interactions including gravity and various sources. In a path integral approach to quantum field theory such a view attributes ‘hard cores’ in the space of field histories to non-renormalizable interactions. Just as with more familiar ‘hard cores’, turning off the interaction does not completely remove all effects of the potential. Consequently the interacting theory is not even continuously connected to the usual free theory, but rather to an alternative ‘pseudo-free’ theory that incorporates the vestiges of the ‘hard cores’. Some insight into what is the significance and interpretation of non-renormalizable interactions can be gleaned from exactly soluble models. Application of this philosophy of non-renormalizable interactions is discussed for the gravitational field in interaction with some standard sources.     

On the renormalizability of a gauge theory of gravitation

One-loop divergences in gauge theory of gravitation with a quadratic Lagrangian are computed. The renormalizability of the theory in the case of Riemannian background is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 43–49, December, 1984.     

On ghost neutrinos in the Einstein-Cartan theory of gravitation

Different characterization of ghost neutrinos in the Einstein-Cartan theory of gravitation are proposed and analyzed.     

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.     

On conformally related fields in Rosen's bimetric gravitation theory

It is shown that the gravitational energy generation vector is conformally invariant. The necessary and sufficient condition for the conformai invariance of the gravitational field equations is found. The conformal transformations of two simple nongravitational energy tensors are considered. It is shown that the conformal factor for metrics conformal to the background is the solution of a simple differential equation.     

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.     

Republication of: 3. On the theory of gravitation

This is the English translation of the first of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917–1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein’s equations. The English translations of the other two papers are published alongside this one. The papers have 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 Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.     

On one new effect of the Einsteinian theory of gravitation

It is shown by using the equation of geodesic deviation that a small test particle, placed in the centre of inertia of a terrestrial spherical satellite, will vibrate if a small initial momentum dⁱ/dsbe given to this particle at a certain moment of the satellite's proper time S=0. These vibrations may be in the satellite's orbital plane and the plane perpendicular to it with the frequencies determined by the formulae (14) and (16). The difference between the periods of these vibrations determined by the formula (20) is one new effect of the Einsteinian theory of gravitation (GTR). The shifting of the point of intersection on the lines of these vibrations corresponds to this difference of periods (20). This shifting, taking place in the time of several complete periods, will be of a distance 10^–6–10^–7 cm if plausible assumptions about the quantities of the test particle velocities and amplitudes are made.     

On the uniqueness of the Newtonian theory as a geometric theory of gravitation

A study is made of geometric theories of gravitation that are consistent with the local validity of Newtonian dynamics. This involves an analysis of the representations of the Galilean group provided by the curvature tensor of a Newtonian spacetime, and by the contravariant mass-momentum tensor. Subject to certain assumptions that are made also in the foundations of general relativity, it is shown that there exists essentially only one such theory that does not place unacceptable restrictions on the mass density of the source. This is the Newtonian theory, generalized by a cosmological term. Any other theory is weaker and is given by a subset of the geometrical equations of the Newtonian theory.