The Inversion of the EINSTEIN-STRAUS Theorem

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 r_b of the comoving radial coordinate r.     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Extremization of mass of charged superdense star models describe by Durgapal type space-time metric

In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g ₄₄=B(1+Cr ²) ⁿ , where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved.     

Second order rotational effect on the oscillation frequencies of V1162 Ori

V1162 is a δ-Scuti type variable star for which a rotational velocity of V  sini=46±4 km s⁻¹ has been observed. The star has been modelled according to its observed parameters and oscillation frequencies. The results obtained by approximating rotation to the first order have been compared with the ones provided by new calculations that include rotation up to the second order. We found that second order rotation term should be included in frequency calculations for comparatively high rotation speeds.     

Radar signal delay in the Dvali-Gabadadze-Porrati gravity in the vicinity of the Sun

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use a space-time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects, we derive expressions for the signal time delays in the vicinity of the Sun. and for various ranges of the angle θ of the signal approach, The time contribution due to DGP correction to the metric is found to be proportional to b ^3/2/c ² r ₀. For r ₀ equal to 5 Mpc and θ in the range [−π/3,π/3], Δt is equal to 0.0001233 ps. This delay is extremely small to be measured by today’s technology but it could be probably measurable by future experiments.     

Interplanetary radar time delays in different theories of gravitation

The first order (in the massm of the central body) time delay is deduced for all theories of gravitation that satisfy the 3-dimensional principle of equivalence in the one-body problem. It is shown that the curvature of the light ray causes no first order time delay but that the first order time delay is sensitive to the non-linear term of a general metric when distancesr are measured by the periods of circular planetary orbits.     

A class of well behaved charged analogues of Vaidya–Tikekar type super-dense star

In the present article a model of well behaved charged superdense star with surface density 2×10¹⁴ gm/cm³ is constructed by considering a static spherically symmetric metric with t=const hypersurfaces as hyperboloid. So far well behaved model described by such metric could not be obtained. Maximum mass of the star is found to be 0.343457M _⊙ and the corresponding radius is 9.57459 km. The red shift at the centre and on the surface are given as 0.068887 and 0.031726 respectively.     

The comoving-frame equation of radiative transfer in relativistic flows

The comoving-frame equations of radiative transfer and moment equations to accurate terms of all orders inv/c are derived in the modified Lagrangian form. The equations exactly describe the interaction of radiation with matter in a relativistically moving medium in flat or curved spacetime. Two specialized sets of equations are presented: (1) the equation of radiative transfer and moment equations accurate to terms of second order (v ²/c ²), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric.     

Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Gravitational perfect fluid collapse in f(R) gravity

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.     

Satellite motion in a non-singular gravitational potential

We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second order. This series contains three terms, the first been the Newtonian potential and the other two, here R ₁ (first order term) and R ₂ (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the second-order disturbing term R ₂ on the perigee and the mean anomaly are 4″.307×10⁻⁹/a, and −2″.533×10⁻¹⁵/a, respectively. These effects are far too small and most likely cannot easily be observed with today’s technology. Numerical evaluation of the low and high frequency effects of the disturbing term R ₂ on low Earth orbiters like GRACE are very small and undetectable by current observational means.     

On Charged Analogues of Buchdahl’S Type Fluid Spheres

In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×10¹⁴ gm cm⁻³. The maximum masses of the star models were found to be 8.223931M_Θ and 8.460857M_Θ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82M_Θ and 4.57M_Θ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.     

The periastron advance in the second post-Newtonian approximation in general relativity

In this paper we present a second order post-Newtonian approximation to the Hamiltonian of theN-body system. Subsequently we improve the well-known Robertson's formula for the perihelion advancement by a correction term of orderc, wherec ^–4 is the velocity of light.     

Tilted Bianchi Type I Models with Heat Conduction Filled with Disordered Radiations of Perfect Fluid in General Relativity

In this paper, we have investigated some tilted Bianchi Type I models with heat conduction filled with disordered radiation of perfect fluid. To get a determinate solution, we have assumed a condition A =(BC) ⁿ between metric potentials. Alternatively we have discussed the case A=(BC) ^1/3 for which tilted nature of the model is preserved. The various and geometrical features with singularities in the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Brans-dicke cosmology and the cosmological constant: The spectrum of vacuum solutions

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).     

Distance in the space of energetically bounded Keplerian orbits

In this paper we derive an explicit, analytic formula for the geodesic distance between two points in the space of bounded Keplerian orbits in a particular topology. The specific topology we use is that of a cone passing through the direct product of two spheres. The two spheres constitute the configuration manifold for the space of bounded orbits of constant energy. We scale these spheres by a factor equal to the semi-major axis of the orbit, forming a linear cone. This five-dimensional manifold inherits a Riemannian metric, which is induced from the Euclidean metric on \mathbbR⁶{\mathbb{R}^6}, the space in which it is embedded. We derive an explicit formula for the geodesic distance between any two points in this space, each point representing a physical, gravitationally bound Keplerian orbit. Finally we derive an expression for the Riemannian metric that we used in terms of classical orbital elements, which may be thought of as local coordinates on our configuration manifold.     

A class of charged analogues of Durgapal and Fuloria superdense star

We obtain a new class of charged super-dense star models after prescribing particular forms of the metric potential g ₄₄ and electric intensity. The metric describing the superdense stars joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. The interior of the stars possess there energy density, pressure, pressure-density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface. In view of the surface density 2×10¹⁴ g/cm³, the heaviest star occupies a mass 5.6996 M _⊙ with its radius 17.0960 km. The red shift at the centre and boundary are found to be 3.5120 and 1.1268 respectively. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982).     

The application of a non-static spherically-symmetric metric to clusters of galaxies

An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10^–36 (k=+1), +3×10^–35 (k=0), +10^–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.     

Compactification and cosmic string phenomenology

A U(1) model of gravitational, Higgs and, gauge fields is analysed. Two phases of the system are considered. In the case with broken symmetry we have the Nielsen-Olesen configuration. In the symmetric phase we find a space-time metric S² × E₁². This appears in full analogy to the Freund-Rubin compactification due to an antisymmeric tensor field. The connection of these structures with cosmic string phenomenology is analysed.     

Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.