Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D ...Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.展开更多
In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric...In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.展开更多
We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models ar...We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models are constructed and analyzed in detail. We found that the state parameter in both the models increases to a higher negative range in an early epoch of the phantom domain and it goes to the positive domain at a late phase of the evolution. The effective cosmological constant remains in a positive domain for both models, which is a good sign of accelerating expansion of the universe.展开更多
Mesonic perfect fluid solutions are found in general relativity with the aid of Einstein’s Rosen cylindrically symmetric space time. A static vacuum model and a non-static cosmological model corresponding to perfect ...Mesonic perfect fluid solutions are found in general relativity with the aid of Einstein’s Rosen cylindrically symmetric space time. A static vacuum model and a non-static cosmological model corresponding to perfect fluid are investigated. The cosmological term Λ is found to be a decreasing function of time which is supported by the result found from recent type Ia Supernovae observations. The various physical and geometrical features of the model are discussed.展开更多
The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential v...The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.展开更多
In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical obj...In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.展开更多
Einstein’s field equations with variable gravitational and cosmological constants are considered in presence of perfect fluid for locally-rotationally-symmetric (LRS) Bianchi type-V space-time discussion in context o...Einstein’s field equations with variable gravitational and cosmological constants are considered in presence of perfect fluid for locally-rotationally-symmetric (LRS) Bianchi type-V space-time discussion in context of the particle creation. We present new shear free solutions for both absence and presence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. We observe that time variation of gravitational and cosmological constant is needed for particle creation phenomena. Moreover, we obtained the particle production rate Γ(t) for this model and discussed in detail.展开更多
In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energ...In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energy-momentum tensor and μ is a constant. Two cosmological models are constructed using the power law expansion and hybrid law cosmology in Bianchi type I universe, where the matter field is considered to be a perfect fluid. It is found that in both the cases the anisotropic behavior is in agreement with the observational results. The state finder diagnostic pair and energy conditions are also calculated and analyzed.展开更多
In this paper, we have studied the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Einstein-Rosen metric with a time dependent gauge function. The cosmological...In this paper, we have studied the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Einstein-Rosen metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are studied.展开更多
Field equations in the presence of perfect fluid distribution are obtained in a scalar tensor theory of gravitation proposed by Brans and Dicke[1] with the aid of Bianchi type-II, VIII & IX metrics. Exact prefect ...Field equations in the presence of perfect fluid distribution are obtained in a scalar tensor theory of gravitation proposed by Brans and Dicke[1] with the aid of Bianchi type-II, VIII & IX metrics. Exact prefect fluid Bianchi type- IX cosmological model is presented since other models doesn’t exist in Brans-Dicke scalar tensor theory of gravitation. Some physical properties of the model are also discussed.展开更多
A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energ...A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.展开更多
Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticit...Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.展开更多
文摘Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.
文摘In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.
文摘We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models are constructed and analyzed in detail. We found that the state parameter in both the models increases to a higher negative range in an early epoch of the phantom domain and it goes to the positive domain at a late phase of the evolution. The effective cosmological constant remains in a positive domain for both models, which is a good sign of accelerating expansion of the universe.
文摘Mesonic perfect fluid solutions are found in general relativity with the aid of Einstein’s Rosen cylindrically symmetric space time. A static vacuum model and a non-static cosmological model corresponding to perfect fluid are investigated. The cosmological term Λ is found to be a decreasing function of time which is supported by the result found from recent type Ia Supernovae observations. The various physical and geometrical features of the model are discussed.
文摘The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.
文摘In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.
文摘Einstein’s field equations with variable gravitational and cosmological constants are considered in presence of perfect fluid for locally-rotationally-symmetric (LRS) Bianchi type-V space-time discussion in context of the particle creation. We present new shear free solutions for both absence and presence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. We observe that time variation of gravitational and cosmological constant is needed for particle creation phenomena. Moreover, we obtained the particle production rate Γ(t) for this model and discussed in detail.
文摘In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energy-momentum tensor and μ is a constant. Two cosmological models are constructed using the power law expansion and hybrid law cosmology in Bianchi type I universe, where the matter field is considered to be a perfect fluid. It is found that in both the cases the anisotropic behavior is in agreement with the observational results. The state finder diagnostic pair and energy conditions are also calculated and analyzed.
文摘In this paper, we have studied the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Einstein-Rosen metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are studied.
文摘Field equations in the presence of perfect fluid distribution are obtained in a scalar tensor theory of gravitation proposed by Brans and Dicke[1] with the aid of Bianchi type-II, VIII & IX metrics. Exact prefect fluid Bianchi type- IX cosmological model is presented since other models doesn’t exist in Brans-Dicke scalar tensor theory of gravitation. Some physical properties of the model are also discussed.
文摘A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.
文摘Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.
