The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivat...The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).展开更多
In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. ...In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.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
If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpfu...If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.展开更多
In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that ...In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that we can calculate the components of the Ricci tensor, Ricci scalar, and Einstein Field Equation directly in an easy way without the need to use general relativity theory hypotheses, principles, and symbols. Formulating the general relativity theory through another theory will make it easier to understand this relativity theory and will help combining it with electromagnetic theory and quantum mechanics easily.展开更多
Ⅰ. INTRODUCTIONIn recent years, on account of the development in superstring theories (which require the background space-time manifold to be (1+9)dimensions )and the application of the Kaluza-Klein theory to the res...Ⅰ. INTRODUCTIONIn recent years, on account of the development in superstring theories (which require the background space-time manifold to be (1+9)dimensions )and the application of the Kaluza-Klein theory to the research of the very early plaases of the universe (1+10) dimensional space-time), some theoretical physicists have displayed much interest in展开更多
This article presents the configuration of strange quark stars in hydrostatic equilibrium considering the Vaidya-Tikekar metric ansatz.The interior of such stars comprises strange quark matter(henceforth SQM),whose eq...This article presents the configuration of strange quark stars in hydrostatic equilibrium considering the Vaidya-Tikekar metric ansatz.The interior of such stars comprises strange quark matter(henceforth SQM),whose equation of state(hencefor orth EoS)is described by the MIT EoS p=1/3(p-4B),where B is the difference between perturbative and non-perturbative vacuum.We have included the mass of the strange quark into the EoS and studied its effect on the overall properties of the strange quark star in this work.It is observed that the maximum mass reaches its highest value when.We have evaluated the range of the maximum mass of the strange quark star by solving the TOV equation for 57.55<B<91.54 MeV/fm^(3)necessary for stable strange quark matter at a zero external pressure condition with respect to neutrons.Maximum mass lies within the range of to when B ranges from 57.55 to 91.54MeV/fm^(3)and ms=0.It is noted that the maximum mass decreases with an increase in.Our model is found suitable for describing the mass of pulsars such as PSR J1614-2230 and Vela X-1 and the secondary objects in the GW170817 event.The model is also useful in predicting the radius of the recently observed pulsars PSR J0030+0451,PSR J0740+6620,and PSR J0952-0607 and the secondary objects in the GW170817 and GW190814 events.Our model is found to be stable with respect to all stability criteria of the stellar configurations and is also stable with respect to small perturbations.展开更多
文摘The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).
基金The Grant-in-Aid for Scientific Research from Nanjing University of ScienceTechnology (AB41409) the NNSF (19771048) of China partly.
文摘In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.
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If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.
文摘In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that we can calculate the components of the Ricci tensor, Ricci scalar, and Einstein Field Equation directly in an easy way without the need to use general relativity theory hypotheses, principles, and symbols. Formulating the general relativity theory through another theory will make it easier to understand this relativity theory and will help combining it with electromagnetic theory and quantum mechanics easily.
文摘Ⅰ. INTRODUCTIONIn recent years, on account of the development in superstring theories (which require the background space-time manifold to be (1+9)dimensions )and the application of the Kaluza-Klein theory to the research of the very early plaases of the universe (1+10) dimensional space-time), some theoretical physicists have displayed much interest in
基金A fellowship has been provided to A.Hakim by Government of West Bengal(G.O.No.52-Edn(B)/5B-15/2017 dated June 7,2017,read with 65-Edn(B)/5-15/2017 dated July 11,2017)to K.B.Goswami by Council of Scientific and Industrial Research,India(vide no.09/1219(0004)/2019-EMR-I)。
文摘This article presents the configuration of strange quark stars in hydrostatic equilibrium considering the Vaidya-Tikekar metric ansatz.The interior of such stars comprises strange quark matter(henceforth SQM),whose equation of state(hencefor orth EoS)is described by the MIT EoS p=1/3(p-4B),where B is the difference between perturbative and non-perturbative vacuum.We have included the mass of the strange quark into the EoS and studied its effect on the overall properties of the strange quark star in this work.It is observed that the maximum mass reaches its highest value when.We have evaluated the range of the maximum mass of the strange quark star by solving the TOV equation for 57.55<B<91.54 MeV/fm^(3)necessary for stable strange quark matter at a zero external pressure condition with respect to neutrons.Maximum mass lies within the range of to when B ranges from 57.55 to 91.54MeV/fm^(3)and ms=0.It is noted that the maximum mass decreases with an increase in.Our model is found suitable for describing the mass of pulsars such as PSR J1614-2230 and Vela X-1 and the secondary objects in the GW170817 event.The model is also useful in predicting the radius of the recently observed pulsars PSR J0030+0451,PSR J0740+6620,and PSR J0952-0607 and the secondary objects in the GW170817 and GW190814 events.Our model is found to be stable with respect to all stability criteria of the stellar configurations and is also stable with respect to small perturbations.
