According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model ...According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.展开更多
In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-...In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.展开更多
We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity （TEGR）. The definition...We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity （TEGR）. The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-NordstrSm black hole. We also calculate the spatial momentum and angular momentum.展开更多
The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time t...The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity （TEGR）, is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.展开更多
In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of ...In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of space-time into positive and negative subspace-time. Here, in the second paper, we continue to analyze each of the four-dimensional vectors of velocity, acceleration, momentum, and forces on the total space-time fabric. According to the approach followed in the first paper. As a result, in the special case, we obtain new transformations for each of the velocity, acceleration, momentum, energy, and forces specific to each subspace-time, which are subject to the positive and negative modified Lorentz transformations described in the first paper. According to these transformations, momentum remains a conserved quantity in the positive subspace and increases in the negative subspace, while the relativistic total energy decreases in the positive subspace and increases in the negative subspace. In the general case, we also have new types of energy-momentum tensor, one for positive subspace-time and the other for negative subspace-time, where the energy density decreases in positive subspace-time and increases in negative subspace-time, and we also obtain new gravitational field equations for each subspace-time.展开更多
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-mom...The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .展开更多
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitra...This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.展开更多
Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor wit...Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.展开更多
We derive two new retarded solutions in the teleparallel theory equivalent to general relativity （TEGR）. One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitati...We derive two new retarded solutions in the teleparallel theory equivalent to general relativity （TEGR）. One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitational energymomentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.展开更多
Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential includ...Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential included with a real number. The relation between the deceleration parameter and Hubble parameter and average scale factor is used in that cosmological model. The effect of the viscosity on the entropy of the universe is utilized by energy momentum tensor with bulk viscous terms in a conservative manner. We obtained a formula for calculating the entropy of the universe in terms of viscosity and used it to compare to the study. Also, various physical and kinematical properties have been discussed.展开更多
In this paper we propose a class of non-stationary solutions of Einstein’s field equations describing an embedded Vaidya-de Sitter solution with a cosmological variable function Λ(u). Vaidya-de Sitter solution is in...In this paper we propose a class of non-stationary solutions of Einstein’s field equations describing an embedded Vaidya-de Sitter solution with a cosmological variable function Λ(u). Vaidya-de Sitter solution is interpreted as the radiating Vaidya black hole which is embedded into the non-stationary de Sitter space with variable Λ(u). The energymomentum tensor of the Vaidya-de Sitter black hole may be expressed as the sum of the energy-momentum tensor of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We also find that the equation of state parameter w= p/ρ = -1 of the non-stationary de Sitter solution holds true in the embedded Vaidya-de Sitter solution. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is type D in the Petrov classification of space-times. The surface gravity, temperature and entropy of the space-time on the cosmological black hole horizon are discussed.展开更多
文摘According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.
文摘In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.
文摘We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity （TEGR）. The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-NordstrSm black hole. We also calculate the spatial momentum and angular momentum.
文摘The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity （TEGR）, is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.
文摘In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of space-time into positive and negative subspace-time. Here, in the second paper, we continue to analyze each of the four-dimensional vectors of velocity, acceleration, momentum, and forces on the total space-time fabric. According to the approach followed in the first paper. As a result, in the special case, we obtain new transformations for each of the velocity, acceleration, momentum, energy, and forces specific to each subspace-time, which are subject to the positive and negative modified Lorentz transformations described in the first paper. According to these transformations, momentum remains a conserved quantity in the positive subspace and increases in the negative subspace, while the relativistic total energy decreases in the positive subspace and increases in the negative subspace. In the general case, we also have new types of energy-momentum tensor, one for positive subspace-time and the other for negative subspace-time, where the energy density decreases in positive subspace-time and increases in negative subspace-time, and we also obtain new gravitational field equations for each subspace-time.
基金the National Natural Science Foundation of China (10072024) the Research Foundation of Liaoning Education Committee (990111001)
文摘The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .
文摘This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.
文摘Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.
文摘We derive two new retarded solutions in the teleparallel theory equivalent to general relativity （TEGR）. One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitational energymomentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.
文摘Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential included with a real number. The relation between the deceleration parameter and Hubble parameter and average scale factor is used in that cosmological model. The effect of the viscosity on the entropy of the universe is utilized by energy momentum tensor with bulk viscous terms in a conservative manner. We obtained a formula for calculating the entropy of the universe in terms of viscosity and used it to compare to the study. Also, various physical and kinematical properties have been discussed.
文摘In this paper we propose a class of non-stationary solutions of Einstein’s field equations describing an embedded Vaidya-de Sitter solution with a cosmological variable function Λ(u). Vaidya-de Sitter solution is interpreted as the radiating Vaidya black hole which is embedded into the non-stationary de Sitter space with variable Λ(u). The energymomentum tensor of the Vaidya-de Sitter black hole may be expressed as the sum of the energy-momentum tensor of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We also find that the equation of state parameter w= p/ρ = -1 of the non-stationary de Sitter solution holds true in the embedded Vaidya-de Sitter solution. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is type D in the Petrov classification of space-times. The surface gravity, temperature and entropy of the space-time on the cosmological black hole horizon are discussed.
