Republication of: On the general relativity theory

This English translation of the paper by H. Weyl, “Zur allgemeinen Relativitätstheorie”, Physikalische Zeitschrift 24, 230–232 (1923), in which he formulated the geometrical foundations of a model of an expanding Universe, has been selected by the Editors of General Relativity and Gravitation for publication in the Golden Oldies series of the journal. The paper is accompanied by an editorial note written by Juergen Ehlers and by Weyl’s brief biography compiled by Andrzej Krasiński from internet sources, with corrections provided by Weyl’s son and grandson.     

Republication of: On the initial value problem of the equations of gravitation

This is an English translation of a paper by Karl Stellmacher, first published in German in 1938, in which he presented the first, correct and successful, formulation of the initial value problem for Einstein’s equations in vacuum and with a dust source. 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 Helmut Friedrich and Stellmacher’s brief biography written by Hubert Goenner.     

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 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 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 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 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.     

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 Møller's tetrad theory of gravitation. Gravitational radiation

In the background of Møller's theory, two energy-momentum complexest andP, are defined. From them, the losses of energy and angular momentum of a nongravitationally bound system due to the radiation of gravitational waves are evaluated. To solve the field equations some approximation procedures are used. The post-Newtonian limit is studied. When the modulus of the coupling constant of the theory is smaller than 10³ and some reasonable conditions are assumed, the results here obtained appear to be identical to those of general relativity. The work performed here would be basic when dealing with some important questions in generalizing Møller's theory.     

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.     

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.     

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.     

A spin-3/2 theory of gravitation

Stimulated by ideas occuring in supergravity, we develop a gauge theory of gravity based on a spin-3/2 Majorana field. Our theory has no metric or vierbein as an elementary field. Classically the theory is in complete agreement with Einstein's metric formulation, but quantum mechanically it differs from ordinary formulations, including supergravity, on the fundamental nature of gravitation. In our approach gravitation arises from a collective effect due to spin-3/2 gravitinos.This essay was awarded the fifth prize for 1978 by the Gravity Research Foundation. (Ed.) Research supported in part by the Department of Energy under contract number EY-76-C-02-3075-190.Alfred P. Sloan Foundation Fellow.     

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.     

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.     

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.     

A bi-metric theory of gravitation. II

The bi-metric theory of gravitation proposed previously is simplified in that the auxiliary conditions are discarded, the two metric tensors being tied together only by means of the boundary conditions. Some of the properties of the field of a particle are investigated; there is no black hole, and it appears that no gravitational collapse can take place. Although the proposed theory and general relativity are at present observationally indistinguishable, some differences are pointed out which may some day be susceptible of observation. An alternative bimetric theory is considered which gives for the precession of the perihelion 5/6 of the value given by general relativity; it seems less satisfactory than the present theory from the aesthetic point of view.