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.     

Maximum mass of a Neutron star in metric theories of gravitation

A method is proposed of finding approximately the equilibrium configurations of nonrotating neutron stars without choosing any particular field equation for the metric. The method consists in choosing interpolation functions for the metric coefficients inside the star and matching them to that of the external metric at the body surface. In particular, the maximum mass a neutron star may have against gravitational collapse is studied, and a good agreement is found when compared with general relativistic results.On a fellowship from the Consejo Nacional de Investigaciones, Científicas y Técnicas de la República Argentina.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.     

The Newtonian limit in a model problem

The Newtonian limit of solutions of a model problem is studied. It is shown that under certain assumptions on the initial data relativistic solutions approach a Newtonian solution as the speed of light tends to infinity. The model problem, although having a much simpler structure than the real equations, shows many of the typical problems arising in the discussion of the Newtonian limit. The method of characteristics is applied and its limitation discussed.     

Errata: A class of metric theories of gravitation of Minkowski spacetime

A mistake which occurred in the derivation of the field equations from the Lagrangian is corrected. Unfortunately many of the expressions given in the article have to be changed, although the results do not change qualitatively, but only quantitatively.     

Bi-metric theories of gravitation

The bi-metric theory recently proposed by Rosen is examined in the case of superdense static objects.     

The structure of the Newtonian limit

We consider a smooth one-parameter family of four-dimensional manifolds X,≥0, each one endowed with a covariant metric g. It is assumed that g is a Lorentz metric for each >0, i.e., the signature of g is (+,−,−,−) for >0, while the limit metric g₀ on X₀ is assumed to be degenerated of rank 1, i.e., the signature of g₀ is (+,0,0,0). We characterize when the limit manifold X₀ inherits the geometric structure of a Newtonian gravitation. The limit manifold X₀ is a Newtonian gravitation if and only if there exist the limits of the Levi-Civita connection , the curvature operator and the contravariant Einstein tensor G² as →0. Moreover, the existence of these limits is characterized in terms of the Taylor expansion of the family {g} with respect to the parameter .     

Interaction in scalar theories of gravitation

It is shown that O. Bergmann's (1956) scalar field theory is similar to G. Nordström's (1912). The interaction term in the former's theory is equivalent to non-linearising the Nordström theory by including twice the energy density of the field as a source term in the Poisson-like equation. It is further shown that, if the interaction term (1+v) in Bergmann's theory is replaced by (1+v)², then the subsequent field equation appears more reasonable in that the energy density (not twice) appears as a source term.     

Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Conformal transformations in scalar-tensor gravitation theories

Conformal transformations in scalar-tensor gravitation theories are investigated in the present paper. It is demonstrated that the field equations of these theories can be expressed in the Vaidya form. A scalar field equation is derived based on the compatibility condition for the field equations. The conformal factor, dilaton, and restrictions on the metric are determined for the diagonal metric of type I in the Bianchi classification. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 10–14, February, 2006.     

The nearly Newtonian regime in non-linear theories of gravity

The present paper reconsiders the Newtonian limit of models of modified gravity including higher order terms in the scalar curvature in the gravitational action. This was studied using the Palatini variational principle in Meng and Wang (Gen. Rel. Grav. 36, 1947 (2004)) and Domínguez and Barraco (Phys. Rev. D 70, 043505 (2004)) with contradicting results. Here a different approach is used, and problems in the previous attempts are pointed out. It is shown that models with negative powers of the scalar curvature, like the ones used to explain the present accelerated expansion, as well as their generalization which include positive powers, can give the correct Newtonian limit, as long as the coefficients of these powers are reasonably small. Some consequences of the performed analysis seem to raise doubts for the way the Newtonian limit was derived in the purely metric approach of fourth order gravity [Dick in Gen. Rel. Grav. 36, 217 (2004)]. Finally, we comment on a recent paper [Olmo in Phys. Rev. D 72, 083505 (2005)] in which the problem of the Newtonian limit of both the purely metric and the Palatini formalism is discussed, using the equivalent Brans–Dicke theory, and with which our results partly disagree.     

The mathematical structure of Newtonian spacetime: Classical dynamics and gravitation

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are timelike vector fields on ) plays a fundamental role in our approach, and the classification of all possible reference frames on is investigated in detail. We succeed in identifying a Lorentzian structure on and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning.     

Plane waves in gauge theories of gravitation

Exact solutions representing pp waves are found in a wide class of gauge theories of gravitation. Algebraic and symmetry properties are investigated and a special case of plane waves is discussed.The work reported in this paper was carried out as part of the Polish Research Project MR-I-7.     

Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg are conserved under the transformation betweeng and the new metrich . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg when the latter is a solution of theories with a quadratic or polynomial Lagrangian.