Mysteries of R^ik=0： A novel paradigm in Einstein＇s theory of gravitation

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321： 151; Astrophys. Space Sei., 2012, 340： 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called ＂vacuum＂ field equations Rik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the Moreover, the resulting theory circumvents the besides explaining some unexplained puzzles. hypothetical dark matter, dark energy or inflation long-standing problems of the standard cosmology     

Cosmological Spacetimes Balanced by a Weyl Geometric Scale Covariant Scalar Field

A Weyl geometric approach to cosmology is explored, with a scalar field φ of (scale) weight −1 as crucial ingredient besides classical matter. Its relation to Jordan-Brans-Dicke theory is analyzed; overlap and differences are discussed. The energy-stress tensor of the basic state of the scalar field consists of a vacuum-like term Λg _{μ ν} with Λ depending on the Weylian scale connection and, indirectly, on matter density. For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the energy-stress tensor of the φ-field can keep space-time geometries in equilibrium. A short glance at observational data, in particular supernovae Ia (Riess et al. in Astrophys. J. 659:98ff, 2007), shows encouraging empirical properties of these models.     

Hawking radiation of scalar and Dirac quanta from a Kerr black hole

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.     

Non-gravitating scalar field in the FRW background

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy–momentum tensor of the scalar field ϕ vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy–momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy–momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space–time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field χ.     

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Antigravitation in gravidynamics

In the bounds of the consistent dynamic interpretation of gravitation (gravidynamics) a gravitational field is divided into two components: scalar and tensor, each interacting with its sources by the same coupling constant. Generated by a massive object, a spherically-symmetrical gravitational field in vacuum has an effect on test bodies as an algebraic sum of attraction (proper gravitation) and repulsion (or antigravitation). The source of the scalar part of the field (or the source of antigravitation) is the trace of the energy-momentum tensor of the gravitating body, which is determined in the end by the total mass M or the total energy Mc ² of this body, including its “coat” consisting of virtual gravitons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bianchi type-V string cosmological models in general relativity

Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.     

Exact Bianchi Type-I Cosmological Models in a Scalar-Tensor Theory

In this paper, a spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid is investigated within the framework of a scalar-tensor theory proposed by Saez and Ballester. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. One of the models is found to generalize a model recently investigated by Reddy et al. (Astrophys. Space Sci. 306:171, 2006). The Einstein’s field equations are solved exactly and the solutions are found to be consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

Thermodynamics of Modified Chaplygin Gas and Tachyonic Field

Here we generalize the results of the work of Myung () in modified Chaplygin gas model and tachyonic field model. Here we have studied the thermodynamical behavior and the equation of state in terms of volume and temperature for both models. We have used the solution and the corresponding equation of state of our previous work (Chattopadhyay et al., Astrophys. Space Sci. 314:41, 2008). for tachyonic field model. We have also studied the thermodynamical stability using thermal equation of state for the tachyonic field model and have shown that there is no critical points during thermodynamical expansion. The determination of T _∗ due to expansion for the tachyonic field have been discussed by assuming some initial conditions. Here, the thermal quantities have been investigated using some reduced parameters.     

Inflation and the Rotation Problem

The effect of an inflaton scalar field on cosmic rotation is discussed. It is shown that any physically reasonable inflaton scalar will dilute the cosmic vorticity by a factor of R^?3γ when the false vacuum decays into matter. Since vorticity decays during inflation as R^3γ-5, this leads to a total decay by a factor of R⁵, which is not dependent on the equation of state of the rotating non-vacuum component of the energy-momentum tensor.     

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

Inheriting geodesic flows

We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors (ψ _;ab ≠ 0) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the quantity ln (R _ab u ^a u ^b ) along the integral curves of the symmetry vector is homogeneous.     

On the Lagrangian Dynamics for the 3D Incompressible Euler Equations

In this paper we study the dynamical behaviors along the particle trajectories for some quantities of the 3D inviscid incompressible fluids. We construct evolution equations satisfied by scalar quantities composed of spectrum of the deformation tensor, the hessian of the pressure and the direction field of the vorticity, and study the dichotomy between the finite time singularity and the long time behaviors of the various scalar quantities.The work was supported partially by the KOSEF Grant no. R01-2005-000-10077-0.     

Cosmological models with constant deceleration parameter

Berman presented elsewhere a law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. By analyzing Einstein, Pryce-Hoyle and Brans-Dicke cosmologies, we derive here the necessary relations in each model, considering a perfect fluid.     

Numerical simulation of 2D granular particles and its analyses by means of the micropolar fluid model

Numerical simulations of two-dimensional granular flows under uniform mean shear and external body torque were performed following the setting of the authors’ previous study [10]. Convergence of the stresses with the increase of coarse-graining length is investigated. Difference R between vorticity field and spin field is controlled by the external torque and the stresses for the region R > 0 is obtained as well as those for R < 0. The symmetry of the stresses under the change of the sign of R is discussed.     

Statefinder diagnostic and stability of modified gravity consistent with holographic and agegraphic dark energy

Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in (Setare in Int J Mod Phys D 17:2219, 2008; Setare in Astrophys Space Sci 326:27, 2010). We also calculate the statefinder parameters which classify our dark energy model.     

FRW in Cosmological Self-creation Theory

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $[\frac{1}{\phi}T^{\mu \nu M}+T^{\mu \nu}(\phi)]_{;\nu}=0$ . We take as a first model the flat FRW metric and with the law of variation for Hubble’s parameter proposal by Berman and Gomide (Nuovo Cimento B 74: 182, 1983), we find solutions to the Einstein field equations by the cases: inflation (γ=?1), radiation ( $\gamma=\frac{1}{3}$ ), stiff matter (γ=1). For the Inflation case the scalar field grows fast and depends strongly of the constant M _γ=?1 that appears in the solution, for the Radiation case, the scalar stop its expansion and then decrease perhaps due to the presence of the first particles. In the Stiff Matter case, the scalar field is decreasing so for a large time, ?→0. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter (γ=1) and flat universe, using the Hamilton-Jacobi scheme.     

Higgs scalar–tensor theory for gravity and the flat rotation curves of spiral galaxies

The scalar–tensor theory of gravity with the Higgs field as scalar field is presented. For central symmetry it reproduces the empirically measured flat rotation curves of galaxies. We approximate the galaxy by a polytropic gas sphere with the polytropic index γ = 2 and a massive core.     

On the lyman problem

This paper attempts to answer Lyman's question (1990) on the non-uniqueness in defining the 3D measure of the boundary vorticity-creation rate. Firstly, a straightforward analysis of the vorticity equation introduces a definition of a general vorticity flux-density tensor and its ‘effective’ part. The approach is strictly based on classical field theory and is independent of the constitutive structure of continuous medium. Secondly, the fundamental question posed by Lyman dealing with the ambiguity of the 3D measure of the boundary vorticity-creation rate for incompressible flow is discussed. It is shown that the original 3D measure (for an incompressible Newtonian fluid defined by Panton 1984), which is reminiscent of an analogy to Fourier's law, is in its character ‘effective’ and plays a crucial role in the prognostic vorticity transport equation. The alternative 3D measure proposed by Lyman includes, on the other hand, a ‘non-effective’ part, which plays a role in the local determination of the ‘effective’ measure as well as in a certain diagnostic integral boundary condition.