Spherically symmetric cosmological perturbations in the de Donder gauge

Cosmological perturbations on a F-R-W background are considered in a modified de Donder gauge. To guarantee the energy-momentum conservation for the perturbations in the de Donder gauge a compatibility condition is obtained. Finally we present the basic equations for the propagation of spherically symmetric perturbations. These equations are the basis for investigating the influence of cosmological epoches on the growing of density contrasts.     

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.     

Bianchi type I cosmological perfect fluid model in scale invariant theory

The intention of this paper is to study the perfect fluid distribution in scale invariant theory of gravity when the space-time is described by Bianchi type I 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 discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Magnetic field of a neutron star with a superconducting quark core in the CFL-phase

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields in the color superconducting core of a neutron star containing a CFL-condensate of diquarks. The interaction of the diquark CFL-condensate with the magnetic and gluomagnetic gauge fields is taken into account. The behavior of the magnetic field in a neutron star is studied by solving the Ginzburg-Landau equations taking correct account of the boundary conditions, including the gluon confinement conditions. The magnetic field distribution in the quark and hadronic phases of a neutron star is found. It is shown that a magnetic field generated in the hadronic phase by the entrainment effect penetrates into the quark core in the form of quark vortex filaments because of the presence of screening Meissner currents. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 87–98 (February 2007).     

General Lagrangian approach to the equations of motion for test particles with internal structure

The equations of motion for test particles with internal structure are derived from a general Lagrange principle. The internal structure of the particles is described by sets of unspecified geometric objects, which transform homogeneously both under coordinate and under gauge transformations. Most of the Lagrangian approaches known in the literature are special cases of our general formalism.     

New exact solutions of Bianchi I,Bianchi III and Kantowski–Sachs spacetimes in scalar-coupled gravity theories via Noether gauge symmetries

The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski–Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using the first integrals corresponding to the obtained Noether gauge symmetries.     

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R ⁿ (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.     

Post-Newtonian approximations in scale covariant gravitation

The scale covariant theory of gravitation, outlined by Dirac (1973), later developed by Canutoet al. (1977), revisited by Maeder and Bouvier (1978, 1979), takes into account the possible relative changes in the system of units associated with different physical interactions; in this respect, it represents a generalization of the General Relativity Theory. In the line of the latter aforementioned papers, we study here the case of a weak gravitational field, well suited to the inner motions of a star or galaxy cluster, in order to see whether the post-Newtonian approximation scheme can consistently fit into the scale covariant formalism. Such a task turns out to be feasible when the gauge terms met in the field equations are handled in an appropriate way, but only if the gauge or metrical connection vector is inversely proportional to cosmic time, as it should be in consequence of the outer boundary condition imposed on the solution of the field equations describing the Newtonian and the first post-Newtonian approximation.     

天文常数中的相对论问题

现代天文观测技术的日新月异、广义相对论的１ＰＮ近似方法在天体力学和天体测量中的广泛应用,使得有必要在１ＰＮ框架中严格而细致地重新审查天文常数系统。在相对论框架里,太阳系天体的质量应当定义为ＢＤ质量,它们的相对变化不超过１０＾－１９,可视为守恒量;引力势满足的方程不再是Ｐｏｉｓｓｏｎ方程而与坐标规范的选择有关,引力势也不再能用传统的球谐函数展开。应当选定一种规范,并且以ＢＤ多极矩作为天文常数。黄赤交     

Dynamics of warm inflation with gauge fields in Bianchi type I universe model

In this paper, we study the dynamics of warm inflation in which slow-roll inflation is driven by non-Abelian gauge fields. To this end, we use the geometry of locally rotationally symmetric Bianchi type I universe model. We construct dynamical equations, i.e., first model field equation, energy conservation equations and equation of motion under slow-roll approximation. In order to discuss inflationary perturbations, we evaluate parameters like scalar and tensor power spectra as well as scalar and tensor spectral indices. We also evaluate inflaton, directional Hubble parameter, slow-roll and perturbation parameters as well as tensor-scalar ratio as a function of inflaton during intermediate and logamediate inflationary eras. It is concluded that anisotropic inflationary universe model with non-Abelian gauge fields remains compatible with WMAP7.     

Cylindrically symmetric cosmologies in Lyra geometry

A class of new exact solutions of the Einstein field equations have been investigated for stationary cylindrically symmetric space-time around a local cosmic string in the theory based on Lyra’s geometry in normal gauge in the presence and absence of an electromagnetic field. The cosmological solutions have been analyzed through various physical and geometrical parameters. It has also been shown that the solutions are space-time inhomogeneous and filled with charged dust.     

On CCGG,the De Donder-Weyl Hamiltonian formulation of canonical gauge gravity

This short paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder-Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical transformation theory. That framework derives, from a few basic physical and mathematical assumptions, equations describing generic matter and gravity dynamics with the spin connection emerging as a Yang Mills-type gauge field. While the interaction of any matter field with spacetime is fixed just by the transformation property of that field, a concrete gravity ansatz is introduced by the choice of the free (kinetic) gravity Hamiltonian. The key elements of this approach are discussed and its implications for particle dynamics and cosmology are presented. New insights: Anomalous Pauli coupling of spinors to curvature and torsion of spacetime, spacetime with (A)dS ground state, inertia, torsion and geometrical vacuum energy, Zero-energy balance of the Universe leading to a vanishing cosmological constant and torsional dark energy.     

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 10¹⁸ G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core. Translated from Astrofizika, Vol. 51, No. 4, pp. 633–646 (November 2008).     

Bianchi type-VI0 cosmological models in certain theories of gravitation

Exact Bianchi type-VI₀ cosmological solutions to Einstein's equations are presented in vacuum and for stiff-matter in the normal gauge for Lyra's geometry and in scalar-tensor theories developed by Saez and Ballester (1985) and Lau and Prokhovnik (1986). Also cosmological solutions are obtained for pure massive strings (p-strings) and for pure geometric strings. The dynamical behaviour of the models have been discussed.     

A family of Coordinate Systems for Reissner-Nordstrom Geometry

In this work we integrate Einstein-Maxwell equations for a point charge, in a coordinate system first considered by Lake. The family of solutions obtained includes various well known metrics. A free metric function acting as a gauge in the solution, is related to the Lorentz contraction factor in infinity, considering a set of geodesic frames. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the definition of mass-energy of a static spherically-symmetric mass in the post-newtonian approximation of general relativity

Recently we (Roy and Rana, 1990a) critically examined the self-consistency of the EIH equations of motion. A static spherically symmetric body as was pointed out there may not appear as a point mass with all its mass concentrated at its centre to a particle placed outside the body. An attempt to analyse this aspect further is made here in the context of the Chandrasekhar gauge. A comparison is also made with the general solutions obtained by Schwarzschild in the standard co-ordinates. Certain difficulties still exist.     

Magnetic Field of a Neutron Star With Color Superconducting Quark Matter Core

The behaviour of the magnetic field of a neutron star with a superconducting quark matter core is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the usual magnetic and to the gluomagnetic gauge fields. We solve the Ginzburg-Landau equations by properly taking into account the boundary conditions, in particular, the gluon confinement condition. We found the distribution of the magnetic field in both the quark and hadronic phases of the neutron star and show that the magnetic field penetrates into the quark core in the form of quark vortices due to the presence of Meissner currents.     

Conformally symmetric Abelian Higgs sunspot and non-metricity of the Sun's spacetime

A U(1)-symmetric Yang-Mills-Higgs (i.e., an Abelian Higgs) sunspot's model is recognized to originate from a massless, complex-valued scalar field coupled minimally to electromagnetic gauge potentials in the background of a (globally)conformally symmetric semi-metric spacetime, whose metric structure is described by the generalized Einstein equations with nonvanishing (positive-valued) cosmological constant. It is shown, in particular, that non-linearity (selfcoupling) of the scalar field appears due to a non-zeroness of the cosmological term, whereas its non-zero vacuum amplitude is induced by the (Ricci scalar) curvature of the Sun's spacetime manifold.     

Dynamical effect of torsion in gravitaional field

In this paper we discuss the dynamical properties of a spinning body in a gravitational gauge theory containing torsion. Formulae are given for the precession of the Earth in the static spherically-symmetric field of the Sun and of the gyroscope. These formulae are valid for any model of gauge theory that includes torsion.     

Correlation between the physical parameters and morphological type of spiral galaxies

Static Friedmann-Robertson-Walker vacuum models are derived in the scale-covariant theory. Specific functional forms are obtained for the gauge function which occurs in the theory. This is in contrast to the nonstatic vacuum solutions where the gauge function is arbitrary.