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1.
We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function F(R)\mathcal{F}(R) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.  相似文献   

2.
We study the Brans-Dicke vacuum field equations in the presence of a cosmological term A. Considering a Friedmann-Robertson-Walker metric with flat spatial sections (k=0), we provide a qualitative analysis of the solutions and investigate its asymptotic properties. The general solution of the field equations for arbitrary values ofw and A is obtained.Work supported by CNPq (Brazil).  相似文献   

3.
A new class of exact solutions of Einstein’s field equations with a bulk viscous fluid for an LRS Bianchi type-Ia obtained by using a time dependent deceleration parameter and cosmological term Λ. The coefficient of bulk viscosity is assumed to be a power function of mass density (ξ=ξ 0 ρ n ). We have obtained a general solution of the field equations from which six models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.   相似文献   

4.
A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electromagnetic field, is obtained.F 12 is the non-vanishing component of the electromagnetic field tensor. To get a determinate solution, we assume the free gravitational field is Petrov type-II non-degenerate. In general, the model represents an expanding, shearing, non-rotating universe in which the flow vector is geodetic. The behaviour of the electromagnetic field tensor together with some geometrical and physical aspect of the model are also discussed.  相似文献   

5.
A. V. Usmanov 《Solar physics》1993,143(2):345-363
An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10R S (R S is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10R S and the Earth's orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10R S (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earth's orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different.  相似文献   

6.
The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.  相似文献   

7.
Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.  相似文献   

8.
A general tetrad fields, with an arbitrary function of radial coordinate, preserving spherical symmetry, is provided. Such tetrad is split into two matrices: The first matrix represents a Local Lorentz Transformation (LLT), which contains an arbitrary function. The second matrix represents a proper tetrad fields which satisfy the field equations of f(T) gravitational theory. This general tetrad is applied to the field equations of f(T). We derive a solution with one constant of integration to the resulting field equations of f(T). This solution gives a vanishing value of the scalar torsion. We calculate the energy associated with this solution to investigate what is the nature of the constant of integration.  相似文献   

9.
We present an approximate solution of global monopole based on Lyra geometry retaining terms of the order 1/3 2 in the energy momentum tensor for a triplet scalar field. Also the gravitational field of the monopole solution has been considered. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

10.
In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f(R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f(R 0) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f(R 0) plays the role of the cosmological constant.  相似文献   

11.
The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n 2 is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion.  相似文献   

12.
The nonlinear pseudo-radial mode of oscillation of a rotating magnetic star is studied. It is shown that for a general rotational field, the coupling between magnetic field and rotation tends to reduce the average rotational energy parameterT. This result in a lowering of the maximum pulsation amplitudeq max, which depends on strength of rotation and magnetic field. The configuration tends, therefore, to a new equilibrium state at lower value ofq max. The analytic solution of the pulsation equation for the case ofy=5/3 in the presence of rotation and magnetic field has also been derived in the Appendix.  相似文献   

13.
We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I1) is studied extensively. The solution (I1) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ b =2×1014 g/cm3, the maximum mass of Neutron star comes out to be 1.34 M Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.  相似文献   

14.
We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. The maximum mass of the Neutron star comes out to be M=1.591 M Θ with radius R b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.  相似文献   

15.
In this article we collect several results related to the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. At first we generalize Whittaker's result of the fourteen powers ofr which lead to intergrability with elliptic functions. We enumerate six more general potentials, including Whittaker's fourteen potentials as particular cases (Sections 2 and 3).Next, we study the stability of the circular solutions, which are the singular solutions of the problem, in Whittaker's terminology. The stability index is computed as a function of the exponentn and its properties are explained, especially in terms of bifurcations with other families of ordinary periodic solutions (Sections 4, 5 and 7). In Section 6, the detailed solution of the inverse cube force problem is given in terms of an auxiliary variable which is similar to the eccentric anomaly of the Kepler problem.Finally, it is shown that the stable singular circular solutions of the central force problem generalize to stable singular elliptic solutions of the two-fixed-center problem. The stability and the bifurcations with other families of periodic solutions of the two-fixed-center problem are also described.  相似文献   

16.
We generalize the well-known analogies between m2φ2 and R + R2 theories to include the selfinteraction λφ4-term for the scalar field. It turns out to be the R + R3 Lagrangian which gives an appropiate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e. g., by linearizing around a ground state the masses of the resp. spin 0-parts concide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L(R), L′L″ ≠ 0, and a minimally coupled scalar field in a general potential.  相似文献   

17.
A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.  相似文献   

18.
We study a perfect fluid Bianchi II models with time varying constants under the self-similarity approach. In the first of the studied model, we consider that only vary G and Λ. The obtained solution is more general that the obtained one for the classical solution since it is valid for an equation of state ω∈(−1,∞) while in the classical solution ω∈(−1/3,1). Taking into account the current observations, we conclude that G must be a growing time function while Λ is a positive decreasing function. In the second of the studied models we consider a variable speed of light (VSL). We obtain a similar solution as in the first model arriving to the conclusions that c must be a growing time function if Λ is a positive decreasing function.  相似文献   

19.
Teleparallel gravity is an equivalent formulation of general relativity in which instead of the Ricci scalar R, one uses the torsion scalar T for the Lagrangian density. Recently teleparallel dark energy has been proposed by Geng et al. (in Phys. Lett. B 704, 384, 2011). They have added quintessence scalar field, allowing also a non-minimal coupling with gravity in the Lagrangian of teleparallel gravity and found that such a non-minimally coupled quintessence theory has a richer structure than the same one in the frame work of general relativity. In the present work we are interested in tachyonic teleparallel dark energy in which scalar field is responsible for dark energy in the frame work of torsion gravity. We find that such a non-minimally coupled tachyon gravity can realize the crossing of the phantom divide line for the effective equation of state. Using the numerical calculations we display such a behavior of the model explicitly.  相似文献   

20.
A most general exact solution to the Einstein-Maxwell equations for static charged perfect fluid is sought in terms of pressure. Subsequently, metrics (e λ and e υ ), matter density and electric intensity are expressible in terms of pressure. Consequently, Pressure is found to be an invertible arbitrary function of ω(=c 1+c 2 r 2), where c 1 and c 2(≠0) are arbitrary constants, and r is the radius of star, i.e. p=p(ω). We present a general solution for charged pressure fluid in terms for ω. We list and discuss some old and new solutions which fall in this category.  相似文献   

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