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1.
For field equations of 4th order, follwing from a Lagrangian “Ricci scalar plus Weyl scalar”, it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = o nad r = ∞ resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme.  相似文献   

2.
The fourth order field equations proposed by TREDER with a linear combination of BACH 's tensor and EINSTEIN 's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry.  相似文献   

3.
“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, Rik = 0, such solutions must be metrics gik(xl) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations Rik – 1/2gikR =–xTik itselves. Therefore if 10 regular functions gik(xl) are given (which the inequalities of LORENTZ -signature fulfil) then these gik define 10 functions Tik(xl) without singularities. But, the matter-tensor Tik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.  相似文献   

4.
According to the equivalence between the FRIEDMANN equation of relativistic cosmology and the condition for the time-independence H = o of the HAMILTON ian H of an isotropic particle-system in the NEWTON ian mechanics (which equivalence is proved in the part I of our paper) we construct the corresponding classical HAMILTON ians to the relativistic world-models. Each cosmological model which is resulting from a physically meaningful gravitation theory must give a FRIEDMANN equation as the cosmological formulation of the time-independence condition of the energy H for the corresponding NEWTON ian N-particle system. In general relativity, EINSTEIN's field equations are including EINSTEIN's strong principle of equivalence and are giving the constance f = o and M = o of the gravitation-number f and of the mass M of the universe additional to FRIEDMANN's equation. – In special relativity, we have fM = o and this MILNE -universe is possessing a NEWTON ian and a general relativistic interpretation, too. – However, if the postulate together with the “cosmological principle” other principles about the world structure, too (p. e. MACH'S or DIRAC'S principle or the “perfect cosmological principle” by the steady-state cosmology), then EINSTEIN'S weak principle of equivalence can be fulfilled, only. In these world models the gravity-mass fM becomes a function of the cosmic time t [d/dt(fM) ± o] and this variability of fM is compatible with the constance H = o of the energy H of the NEWTON ian particle-system. For flat three-dimensional cosmological spaces (with H = Ḣ = o) a creation of rest-mass (M > o) is possible. This creation is the pecularity of the steady-state cosmos (with M > o, f = o) and of JORDAN'S cosmos (with M > o, f < o). The MACH -EINSTEIN -doctrine about the perfect determination of the inertia and of the space-time-metric by the cosmic gravitation is founded on the substitution of the NEWTON ian HAMILTON ian by a GAUSS -RIEMANN ian gravitation potential U*(rAB' vAB) (TREDER 1972). Therefore, the FRIEDMANN equation for a universe with MACH'S principle is resulting from the analytical expression of the time-independence of this RIEMANNian potential U* = 0. In the case of such MACH-EINSTEIN's-Universes EINSTEIN'S condition 3fM = c8r between the mass A4 and the radius Y of the universe is valid additional to FRIEDMANN'S equation. For these universes, the EINSTEIN condition determinates the instantaneous value of the gravitation-number f. - The explicite form of the conditions H = o or h' = o gives the equation of motion for the cosmic fundamental particles with attraction and repulsion forces, generally.  相似文献   

5.
We consider the inversion of a problem put by A. EINSTEIN and E. G. STRAUS , that is, we ask for restrictions on the scaling factor R(t) of the ROBERTSON WALKER metric and the functions H2(r') and A2(r') of a spherically symmetric and static vacuum metric, which are consequences of the requirement that the vacuum metric shall pass continuously differentiable into the ROBERTSON WALKER metric at a certain value rb of the comoving radial coordinate r.  相似文献   

6.
The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92M Θ with radius r b ≈17.15 km and the surface red shift Z b ≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.  相似文献   

7.
We have obtained static and spherically symmetric self-gravitating solution of the field equations for anisotropic distribution of matter in higher- dimensional in the context of Einstein’s general theory of relativity. This work is an extension of the previous work of Hector Rago (Astrophys. Space Sci. 183:333, 1991) for four dimensional space-time. The solutions are matched to the analytical solutions for spherically symmetric self gravitating distribution of anisotropic matter obtained by Hector Rago (1991) for n=2.  相似文献   

8.
Assuming that the physical 3-spacet = const in a superdense star is spheroidal, a static spherically symmetric model based on an exact solution of Einstein’s equations is given which will permit densities of the order of 2 × 1014 gm cm-3, radii of the order of a few kilometers and masses up to about four times the solar mass.  相似文献   

9.
The equations governing the two-fluid spherically symmetric models of the solar wind have been solved numerically for a wide range of base conditions. As predicted from an asymptotic analysis we find a whole domain of solutions which are asymptotically adiabatic with the proton and electron temperatures tending to equality and varying like r - 4/3. In these 4/3 solutions the electron and proton heat conduction is asymptotically negligible and if it is neglected the resulting equations can be integrated analytically and shown to have the 4/3, 4/3 behaviour.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.  相似文献   

10.
First, in connection with their construction due to HADAMARD, the mathematical and physical meaning of covariant Green's functions in relativistic gravitational fields - according to EINSTEIN: on curved space-time - is discussed. Then, in the case of a general static spherically symmetric space-time the construction equations for a scalar Green's function are cast into symmetry-adapted form providing a convenient starting point for an explicit calculation of the Hadámard building elements. In applying the obtained basic scheme to a special one-parameter family of model metrics one succeeds in advancing to the explicit exact calculation of tail-term coefficients of a massless Green's function which are simultaneously coefficients in the Schwinger-De Witt expansion of the Feynman propagator for the corresponding massive Klein-Gordon equation on curved space-time.  相似文献   

11.
In this article we have derived a set of three static spherical symmetric well behaved solutions of Einstein-Maxwell field equations is obtained for a specific choice of electric field involving a parameter K. The solutions so obtained can be seen as a charge analogue of the neutral solution due to Vlasenko and Pronin. The physical features of solutions so obtained and that of Vlasenko and Pronin are investigated subject to the reality and the causality conditions i.e. Pressure, density (greater than pressure), pressure-density ratio and velocity of sound (less than the velocity of light) are positive and monotonically decreasing and the electric intensity is monotonically increasing in nature away from the centre. The maximum mass and radius occupied by the neutral solution are 2.1434 M Θ and 16.7300 km respectively. For the charged solution, overall maximum mass and corresponding radius are found to be 6.8714 M Θ and 20.6166 km respectively (for K=1.343).  相似文献   

12.
Detailed analyses by independent research groups over several decades reveal a significant discrepancy between the observed rate of periastron advance in the detached eclipsing binary star systems DI Herculis and V541 Cygni and the values theoretically predicted from the combined classical and general relativistic effects. A modification to Newton’s gravitational theory is proposed in this investigation to account for these discrepancies, and is represented by
F = - \fracGm1m2r3r - \fracGom1m2r2r\mathbf{F} = - \frac{Gm_{1}m_{2}}{r^{3}}\boldsymbol{r} - \frac{G_{o}m_{1}m_{2}}{r^{2}}\boldsymbol{r}  相似文献   

13.
We discuss the excitation of polar motion by earthquake displacement field. Instead of the usual static equilibrium equations in the literature, we use an improved set as given in /1/, which guarantee continuity at the core-mantle boundary. We take the parameter values of three earthquakes from /2/.To obviate the singularity at r = 0, we use asymptotic solutions by power series within a small sphere around the centre. Outisde this sphere, the equations are numerically integrated by the Runge-Kutta algorithm. Our equations /1/ gave polar shifts some 3 times larger than Dahlen's equations /2/.  相似文献   

14.
Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant Λ to be a space-variable scalar, viz., Λ=Λ(r). Two cases are examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., ρ+p=0 is not always required for constructing electromagnetic mass models.  相似文献   

15.
Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in D-dimensional gravity with a chain of n Ricci-flat internal spaces are considered. Their properties and special cases are discussed. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.  相似文献   

16.
In the previous paper (Li et al. in Phys. Lett. B 666:125–130, 2008), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinormal modes by WKB method in this paper. The numerical results show that both the real part of the quasinormal frequencies and the imaginary part decrease as the state parameter w, for scalar and gravitational perturbations. And we also show variations of quasinormal frequencies of scalar and gravitational fields via different ε (deficit solid angel parameter) and different ρ 0 (density of static spherically-symmetric quintessence-like matter at r=1), respectively.  相似文献   

17.
In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential \(z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)\) and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for \(\eta =1,~2\).  相似文献   

18.
The requirement that near a singular point of the equations of motion the power series expansions of the old variables in terms of the new ones start with second order terms leads to the transformation z = sin21/2w related to that of THIELE -BURRAU . Using this new transformation, a derivation of the regularized equations of motion is given. The original as well as the regularized equations of motion are of interest, for example, for calculating the initial values of the orbital elements for SCHWARZSCHILD's periodic solutions (LEIMANIS and OLUND 1972).  相似文献   

19.
Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr arrbwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr a andr b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr o , Examples of Green's functions are given for the caser a =0,r b = and derived for the cases of finiter a andr b . The diffusion coefficient is assumed of the form = o(p)r b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.  相似文献   

20.
A three-dimensional (non-axisymmetric) model for the solar mean magnetic field generation is studied. The sources of generation are the differential rotation and mean helicity in the convective shell. The system is described by two equations of the first order in time and the fourth order in space coordinates. The solution is sought for in the form of expansion over the spherical function Ynm. The modes of different m are separated. A finite-difference scheme similar to the Peaceman-Rachford scheme is constructed so to find coefficients of the expansion depending on the time and radial coordinates. It is shown that a mode with a smaller azimuthal number m is primarily excited. The axisymmetric mode m = o describes the 22 year solar cycle oscillations. The modes of m o have no such periodicity, the oscillate with a period of rotation of the low boundary of the solar convective shell, The solutions which are symmetric relative to the equator plane are excited more easily compared with the antisymmetrical ones. The results obtained are confronted to the observational picture of the non-axisymmetric large-scale solar magnetic fields.  相似文献   

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