Covariant Theory Of Gravitation Research Articles

The relativistic uniform model: the metric of the covariant theory of gravitation inside a body

The relativistic uniform model: the metric of the covariant theory of gravitation inside a body

A dissertation on General Covariance and its application in particle physics

In this paper, we provide a concise overview on the principle of General Covariance, one of the fundamental cornerstones of Einstein’s General Relativity. We retrace all the steps that led to the final settlement of a generally covariant theory of gravitation, dwelling specifically on the significance of the well-known “hole argument”. In addition, we discuss about the importance of General Covariance in connection with some recent claims in literature revolving around particle physics. In particular, we summarize the results associated with the decay of accelerated protons.

Anisotropic bianchi V cosmological model in Scale Covariant Theory of Gravitation with a time-variable deceleration parameter

In this paper we solve the field equations for Scale covariant theory of gravitation which was introduced by Caunato et al. [1], for Bianchi V line element in the presence of perfect fluid medium. Here the deceleration parameter is considered to be time dependent which gives the average scale factor a(t)=[sinh⁡(βt)]1/n, where n and β are positive constants. This value of average scale factor is the key expression for solving the field equations. Using the recent observational value of q0=−0.52−0.04+0.08 and H0=69.2±1.2 derived from BAO/CMB and H(z) data by Santos et al. (2016) [46], we have evaluated three different pairs of (n,β). We observe that the model represents a phase transition from early deceleration to a present accelerating phase for a particular choice of the pair (n=2,β=92.75). Applying some recently developed diagnostic tools like jerk parameter and statefinders, we find that the derived model is exactly in accordance with standard ΛCDM model. Along with these, many physical, geometric and kinematic properties of the model are thoroughly studied and found consistent with recent observations.

Dark energy and modified scale covariant theory of gravitation

Taking up four model universes we study the behaviour and contribution of dark energy to the accelerated expansion of the universe, in the modified scale covariant theory of gravitation. Here, it is seen that though this modified theory may be a cause of the accelerated expansion it cannot totally outcast the contribution of dark energy in causing the accelerated expansion. In one case the dark energy is found to be the sole cause of the accelerated expansion. The dark energy contained in these models come out to be of the ΛCDM type and quintessence type comparable to the modern observations. Some of the models originated with a big bang, the dark energy being prevalent inside the universe before the evolution of this era. One of the models predicts big rip singularity, though at a very distant future. It is interestingly found that the interaction between the dark energy and the other part of the universe containing different matters is enticed and enhanced by the gauge function ϕ(t) here.

The Mass Hierarchy in the Relativistic Uniform System

The analysis of the relativistic uniform system in the framework of the covariant theory of gravitation leads to five different masses of the physical system, in which the particles are bound together by means of the electromagnetic and gravitational fields, the acceleration field and the pressure field. In this case it turns out that the system's gravitational mass is equal to the sum of the invariant masses of all the system's particles, and the system's inertial mass is less than the gravitational mass by the value of the system's binding mass-energy.

Energy and Metric Gauging in the Covariant Theory of Gravitation

Relations for the relativistic energy and metric are analyzed inside and outside the body in the framework of the covariant theory of gravitation. The methods of optimal energy gauging and equations for the metric are chosen. It is shown that for the matter inside the body a procedure is required to average the physical quantities, including the cosmological constant and the scalar curvature. For the case of the relativistic uniform system, the cosmological constant and the scalar curvature are explicitly calculated, which turn out to be constant values inside the body and are assumed to be equal to zero outside the body. Comparison of the cosmological constants inside a proton, a neutron star and in the observable Universe allows us to explain the cosmological constant problem arising in the Lambda-CDM model

Dynamics of Bianchi type-V anisotropic dark energy cosmological model in a scale covariant theory of gravitation

This paper is devoted to the discussion of dynamical properties of anisotropic dark energy cosmological model of the universe in a Bianchi type-V space time in the framework of scale covariant theory of gravitation formulated by Canuto et al.(phys.Rev.Lett.39:429,1977).A dark energy cosmological model is presented by solving the field equations of this theory by using some physically viable conditions. The dynamics of the model is studied by computing the cosmological parameters, dark energy density, equation of state(EoS) parameter, skewness parameters, deceleration parameter and the jerk parameter. This being a scalar field model gives us the quintessence model of the universe which describes a significant dark energy candidate of our accelerating universe. All the physical quantities discussed are in agreement with the recent cosmological observations.

The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation

For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the tensor invariant of the gravitational field. The problem of inaccuracy of the use of the field’s stress-energy tensors for calculating the system’s mass and energy is considered. The found expressions for the gravitational field strengths inside and outside the system allow us to explain the occurrence of the large-scale structure of the observable Universe, and also to relate the energy density of gravitons in the vacuum field with the limiting mass density inside the proton. Both the Universe and the proton turn out to be relativistic uniform systems with the maximum possible parameters. The described approach allows us to calculate the maximum possible Lorentz factor of the matter particles at the center of the neutron star and at the center of the proton, and also to estimate the radius of action of the strong and ordinary gravitation in cosmological space.

Covariant theory of gravitation in the framework of special relativity

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common - these similarities, in fact, are just a requirement of special relativity that must apply to any physically (...)

The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation

For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the tensor invariant of the gravitational field. The problem of inaccuracy of the use of the field’s stress-energy tensors for calculating the system’s mass and energy is considered. The found expressions for the gravitational field strengths inside and outside the system allow us to explain the occurrence of the large-scale structure of the observable Universe, and also to relate the energy density of gravitons in the vacuum field with the limiting mass density inside the proton. Both the Universe and the proton turn out to be relativistic uniform systems with the maximum possible parameters. The described approach allows us to calculate the maximum possible Lorentz factor of the matter particles at the center of the neutron star and at the center of the proton, and also to estimate the radius of action of the strong and ordinary gravitation in cosmological space.

Spherically symmetric five dimensional cosmological model in scale covariant theory of gravitation

A higher dimensional cosmological model filled with perfect fluid source in the frame work of scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977) is considered. A determinate solution of the field equations is obtained using a relation between the metric potentials. The physical behavior of the model is discussed by computing the physical and kinematical parameters of the model.

Relativistic energy and mass in the weak field limit

Within the framework of the covariant theory of gravitation (CTG) the energy is calculated for a system with continuously distributed matter, taking into account the contribution of the gravitational and electromagnetic fields and the contribution of the pressure and acceleration fields. The total energy of all the fields is equal to zero, and the system’s energy is formed from the energy of the particles, which are under the influence of these fields. From the expression for the energy the inertial M and gravitational mg masses of the system are found. These masses are compared with mass mb, obtained by integrating the density over the volume, and with the total mass m’ of the body particles scattered to infinity in order to make the energy of macroscopic fundamental fields equal to zero. The ratio for the masses is obtained: m’ = M < mb = mg . From this the possibility of non-radiative ideal spherical collapse follows, when the system’s mass M does not change during the collapse. In addition, the mass of the system is less than the gravitational mass. In contrast, in the general theory of relativity (GTR) the ratio for masses is obtained in a different form: M = mg < mb < m’. In CTG the electromagnetic field energy reduces the gravitational mass and in GTR, on the contrary, increases. In order to verify the obtained results it is suggested to conduct an experiment on measuring the change of the gravitational mass of the body with increasing its electrical charge.

The Pioneer anomaly in covariant theory of gravitation

The difference of equations of motion in the covariant theory of gravitation and in the general theory of relativity is used to explain the Pioneer anomaly. Calculation shows that the velocities of a spacecraft in both theories at equal distances can differ by several centimetres per second. This leads also to a possible explanation of the flyby anomaly and comet disturbances, which are not taken into account by the general theory of relativity.

Kantowski-Sachs bulk viscous string cosmological model in a scale covariant theory of gravitation

Spatially homogeneous and anisotropic Kantowski-Sachs space-time is considered in the scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977) in the presence of bulk viscous fluid containing one dimensional cosmic strings. A determinate solution of the field equations of this theory is presented using the special law of variation proposed by Bermann (Nuovo Cimento B74:183, 1983). We have also used the proportionality of shear scalar to the scalar expansion of the space time. The solution obtained represents a bulk viscous string cosmological model in this theory. Some physical and kinematical properties of the model are also discussed.

Kantowski-Sachs cosmological model with anisotropic dark energy in scale covariant theory of gravitation

In this paper, we have investigated Kantowski-Sachs space-time in the presence of anisotropic fluid with variable equation of state (EoS) parameter and constant deceleration parameter in the scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). We have found a determinate solution of the field equations of the theory using variation law for Hubble’s parameter given by Bermann (Nuvo Cimento 74:182, 1983). Our solution represents Kantowski-Sachs dark energy model in this theory. The physical and kinematical properties of the model are also discussed.

The Hamiltonian in Covariant Theory of Gravitation

In the framework of covariant theory of gravitation the Euler-Lagrange equations are written and equations of motion are determined by using the Lagrange function, in the case of small test particle and in the case of continuously distributed matter. From the Lagrangian transition to the Hamiltonian was done, which is expressed through three-dimensional generalized momentum in explicit form, and also is defined by the 4-velocity, scalar potentials and strengths of gravitational and electromagnetic fields, taking into account the metric. The definition of generalized 4-velocity, and the description of its application to the principle of least action and to Hamiltonian is done. The existence of a 4-vector of the Hamiltonian is assumed and the problem of mass is investigated. To characterize the properties of mass we introduce three different masses, one of which is connected with the rest energy, another is the observed mass, and the third mass is determined without taking into account the energy of macroscopic fields. It is shown that the action function has the physical meaning of the function describing the change of such intrinsic properties as the rate of proper time and rate of rise of phase angle in periodic processes. Key words: Euler-Lagrange equations; Lagrangian; Hamiltonian; Generalized momentum; Generalized 4-velocity; Equations of motion

Energy, momentum, mass, and velocity of a moving body in the light of gravitomagnetic theory

In the weak-field approximation of the covariant theory of gravitation the 4/3 problem is formulated for internal and external gravitational fields of a body in the form of a uniform ball. The dependence of the energy and the mass of the moving body on the energy of the field accompanying the body, as well as the dependence on the characteristic size of the body are described. Additions in the energy and the momentum of the system, defined by the energy and momentum of the gravitational and electromagnetic fields, associated with the body, are explicitly calculated. The conclusion is made that the energy and the mass of the system can be described through the energy of ordinary and strong gravitation and through the energies of electromagnetic fields of particles that compose the body.

The Metric outside a Fixed Charged Body in the Covariant Theory of Gravitation

The metric outside a charged body is calculated. As part of the given approach it is shown that the gravitational and electromagnetic fields are equally involved in the formation of the metric tensor components. Andthe contribution of fields in the metric is proportional to the energy of these fields. From equations for the metric it follows that the metric tensor components are determined up to two constants.

Bianchi type-V bulk viscous string cosmological model in scale-covariant theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-V space-time is considered in the frame work of a scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977) when the matter sources is a bulk viscous fluid containing one dimensional cos- mic strings. Using some physically plausible conditions, we have obtained a determinate solution of the field equations of the theory which represents a Bianchi type-V bulk viscous string cosmological model in this theory. Some physical and kinematical properties of the model are also discussed.

Magnetized anisotropic dark energy cosmological models in scale covariant theory of gravitation

In the present paper, we have investigated Bianchi type II, VIII and IX spacetime in the presence of magnetized anisotropic dark energy in the Scale covariant theory of gravitation. Exact solution of the field equations are obtained by assuming the expansion anisotropy (the ratio of shear scalar to expansion scalar) to be a function of average scale factor. The isotropy of the fluid, space and expansion are examined.