The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance.

Slightly Bimetric Gravitation

A theory with variable gravitational constant, based on the bimetric formulation of general relativity, is suggested. It is in agreement with the Newtonian and post-Newtonian approximations of the theory of gravitation when the theory parameter |ζ|≫4×10−6. The statical spherical-symmetric distribution of gravitating masses is investigated. It is shown that the total action (including the own gravitational field of the system)S=−Mτ, where τ is the time in the remote system of reference, relative to which the celestial body is in rest. In the Brans-Dicke theory |ζ|≫1 andS≠−Mτ. The Tolman formula for the massM in the Einstein theory is also valid in the suggestedGeneralized Bimetric Theory of Gravitation. External analytical and internal numerical solutions of the field equations are found for the case of incompressible matter. It is shown that static and supermassive configurations may exist if −0.13≲ζ<0.

A New Approach to the Theory with Variable Gravitational Constant

We consider here the structure of rotating compact objects endowed with a magnetic field in general relativity as models of pulsars. We discuss the structure of rotating stars in the framework of Hartle, taking different realistic equations of state, and study their effects on bulk properties of stars. We consider the possibility of rotating stars with a quark matter core. We also analyse the structure of the magnetic field in the interior of the star, as affected by different equations of state, as well as due to rotation.

https://iopscience.iop.org/article/10.1088/0264-9381/15/10/016/pdf

Rotating compact objects with magnetic fields

We construct a class of nuclear equations of state based on a schematic potential model, that originates from the work of Prakash et al.,1 which reproduce the results of most microscopic calculations. The equations of state are used as input for solving the Tolman–Oppenheimer–Volkov equations for the corresponding neutron stars. The potential part contribution of the symmetry energy to the total energy is parametrized in a generalized form both for low and high values of the baryon density. Special attention is devoted to the construction of the symmetry energy in order to reproduce the results of most microscopic calculations of dense nuclear matter. The obtained nuclear equations of state are applied for the systematic study of the global properties of a neutron star (masses, radii and composition). The calculated masses and radii of the neutron stars are plotted as a function of the potential part parameters of the symmetry energy. A linear relation between these parameters, the radius and the maximum mass of the neutron star is obtained. In addition, a linear relation between the radius and the derivative of the symmetry energy near the saturation density is found. We also address the problem of the existence of correlation between the pressure near the saturation density and the radius.

Nuclear symmetry energy effects on neutron stars properties

We consider here the structure of rotating compact objects endowed with a magnetic field in general relativity as models of pulsars. We discuss first the structure of rotating stars in the framework of Hartle taking different realistic equations of state and study their effects on bulk properties of the star. We consider the possibilty of rotating stars with a quark matter core. We further analyse the structure of the magnetic field in the interior of the star as affected by different equations of state as well as due to rotation.

http://arxiv.org/pdf/astro-ph/9805146.pdf

During the last two decades the theory of degenerate stellar configurations has been developed in works by Ambartsumian and Sahakian, as well as in some other papers. This article is further progress in this direction.

Theory of Superdense Matter and Degenerate Stellar Configurations

The gravitation theory is considered in bimetric formulation with a Lagrangian of the most common type and quadratic with respect to the derivativesgik/l of the metric tensor. Restrictions on the dimensionless parameters of the theory are found, basing on the comparison with the Newtonian theory and the analysis of corresponding observational data in the vicinity of the solar system. Propagation of the weak gravitation waves is investigated in the outside gravitational field.

The Gravitation Theory in Bimetric Formulation

A theory of gravitation with a flat background metric and a dynamical variableφ (variable gravitational constant) is investigated. It is shown that such bimetric scalar-tensor theory (BSTT) generalized GR as all the solutions of GR equations andφ(x) = constant satisfy BSTT equations, firstly, and BSTT equations contain non-Einstein solutions with the variableφ, secondly. Due to this fact, the problem on the agreement of BSTT with the observational data is reduced to the problem on the agreement of GR with the observational data and to the interpretation of the solutions with the variableφ. The latter may prove useful for the prediction of new effects. Examples of such effects are discussed.

Is there GR in the bimetric scalar-tensor theory of gravitation?

In part I we suggested an approximate equation to determine the contribution of relativistic effects to the moment of inertia of a superdense star. In the present paper it is tested on model neutron stars with nine different variants of the equation of state of superdense matter. It is established that the approximation error does not exceed 5% for stable configurations. A more accurate version of the Ravenhall—Pethick equation [D. G. Ravenhall and C. J. Pethick, Astrophys. J., 424, 846 (1994)] for the moment of inertia as a function of the mass and radius of a neutron star is derived.

Moment of inertia of a neutron star. II. Relativistic corrections

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension τ
 ik
 . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor τ
 ik
 is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved. The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor τ
 ik
 is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/ɛ,b=p
⊥/ɛ (ɛ,p, p
⊥ are the density of the vacuum energy and of its pressures in the radial and transverse directions) and ω determining the vacuum elastic properties. Generally speaking, they depend on the valueP/ρc2 in the stellar centre where ϱ is the mass density. From general physical considerations it is shown that 0 ≤ ω ≤ 1 + lim
P→∞ (l/q). The field equations are solved for the simple version of the theoryb=−a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.

L. Sh. Grigorian

Papers

Theory of Superdense Matter and Degenerate Stellar Configurations

The Gravitation Theory in Bimetric Formulation

Is there GR in the bimetric scalar-tensor theory of gravitation?

Moment of inertia of a neutron star. II. Relativistic corrections

Phenomenological Theory of Gravitational Vacuum