Bijan Saha
Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. Using the nonlinear spinor field corresponding to different types of perfect fluid or dark energy as a source of gravitational field, evolution of a Bianchi type-I universe has been illustrated.
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Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. Exploiting the spinor description of perfect fluid and dark energy evolution of the Universe given by an anisotropic Bianchi type-I (BI) or isotropic Friedmann-Robertson-Walker (FRW) one has been studied.
Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. We have considered two cases where the spinor field nonlinearity occurs either as a result of self-action or due to the interaction with a scalar field.
Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied.
We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field. For such a configuration, we find a two-parametric family of static regular solutions describing compact objects whose masses and sizes are determined by the central density of the spinor fluid and the mass of the spinor field. Using the similarity method, we consider a gravitational collapse of an initially uniform system consisting of the spinor fluid. We es…
Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied. It should be emphasized the absence of initial singularity for some types of solutions and also the isotropic mode of space-time expansion in some special cases.
We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $λF$, with $λ$ being a self-coupling constant and $F$ being a function of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. This system is so…
We consider a self-consistent system of spinor and scalar fields within the framework of a Bianchi type I gravitational field filled with viscous fluid in presence of a $Λ$ term. Exact self-consistent solutions to the corresponding spinor, scalar and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.
The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in presence of a viscous fluid and $Λ$ term with the spinor field nonlinearity being some arbitrary functions of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$, generates a multi-parametric system of ordinary differential equations \cite{saharrp,grqcnlsp}. A qualitative analysis of the system in question has been thoroughly carried out. A complete qualitative classification of the mode of evolution of the universe given by the corresponding dynamic system has been ill…
Self-consistent system of spinor, scalar and BI gravitational fields in presence of magneto-fluid and $Λ$-term is considered. Assuming that the expansion of the BI universe is proportional to the $σ_1^1$ component of the shear tensor, exact solutions for the metric functions, as well as for scalar and spinor fields are obtained. For a non-positive $Λ$ the initially anisotropic space-time becomes isotropic one in the process of expansion, whereas, for $Λ> 0$ an oscillatory mode of expansion of the BI model occurs.
Mixed invariants are used to classify the Riemann spinor in the case of Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these mixed invariants provide information as to the relative orientation of the gravitational and electromagnetic principal null directions. Consideration of the perfect fluid case leads to some results about the behaviour of the Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.
The study of a self-consistent system of interacting spinor and scalar fields within the scope of a Bianchi type I (BI) gravitational field in presence of a viscous fluid and $Λ$ term has been carried out. The system of equations defining the evolution of the volume scale of BI universe, energy density and corresponding Hubble constant has been derived. The system in question has been thoroughly studied qualitatively. Corresponding solutions are graphically illustrated. The system in question is also studied from the view point of blow up. It has been shown that the blow up takes place only in…
A self-consistent system of interaction nonlinear spinor and scalar fields within the scope of a BI cosmological model filled with perfect fluid is considered. The role of spinor field in the evolution of the Universe is studied. It is shown that the spinor field nonlinearity can generate a negative effective pressure, which can be seen as an alternative source for late time acceleration of the Universe.
Classical Spinors on Curved Spacetime: applications to Cosmology and Astrophysics
本文研究旋量模型在宇宙学背景下的应用，分析其描述暗物质和暗能量的行为，并探讨旋量流的应力能张量在不同条件下的表现，以及通过(1+3)分解方法分析标量宇宙扰动。
Flagpole and flag-dipole spinors are particular classes of spinor fields that has been recently used in different branches of theoretical physics. In this paper, we study the possibility and consequences of these spinor fields to induce an underlying fluid flow structure in the background of Kerr spacetimes. We show that flag-dipole spinor fields are solutions of the equations of motion in this context. To our knowledge, this is the second time that this class of spinor field appears as a physical solution, the first one occurring as a solution of the Dirac equation in ESK gravities.
Within general relativity, we construct sequences of rapidly rotating Dirac stars consisting of a spinor fluid described by an effective equation of state. We find the physically relevant domain of stable configurations and calculate their principal characteristics which are completely determined by the central density of the spinor fluid, the mass of the nonlinear spinor field, and the velocity of rotation. It is demonstrated that for a certain choice of the spinor field mass, the main physical characteristics of the Dirac stars are close to those that are typical of rotating neutron stars.
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in thi…
We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.
Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.
We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition is examined for this family of metrics, and the macroscopic conditions for physical reality are accurately tested for some specific solutions.
Self-consistent system of spinor, scalar and BI gravitational fields is considered. Exact solutions to the field equations in terms of volume scale of the BI metric are obtained. Einstein field equations in account of the cosmological constant $Λ$ and perfect fluid are studied. Oscillatory mode of expansion of the universe is obtained. It is shown that for the interaction term being a power function of the invariants of bilinear spinor forms and $Λ> 0$ and given other parameters, e.g., coupling constant, spinor mass etc., there exists a finite range of integration constant which generates osci…
We revisit certain features of an assumed spherically symmetric perfect fluid dark matter halo in the light of the observed data of our galaxy
In this paper, by applying Newman-Janis algorithm in spherical symmetric metrics, a class of embedded rotating solutions of field equations is presented. These solutions admit non-perfect fluids
We present a new exact perfect fluid interior solution for a particular scalar-tensor theory. The solution is regular everywhere and has a well defined boundary where the fluid pressure vanishes. The metric and the dilaton field match continuously the external solution.
A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.
The first static spherically symmetric perfect fluid solution with constant density was found by Schwarzschild in 1918. Generically, perfect fluid spheres are interesting because they are first approximations to any attempt at building a realistic model for a general relativistic star. Over the past 90 years a confusing tangle of specific perfect fluid spheres has been discovered, with most of these examples seemingly independent from each other. To bring some order to this collection, we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. The…
Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. Exploiting the spinor description of perfect fluid and dark energy evolution of the Universe given by an anisotropic Bianchi type-VI, VI$_0$, V, III, I or isotropic Friedmann-Robertson-Walker (FRW) one has been studied. It is shown that due to some restrictions on metric functions, initial anisotropy in the models Bianchi type-VI, VI$_0$, V and III does not die away, while the anisotropic Bianchi type-I models evolves into the isotropic one.
We report several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. In addition, we report new ``solution generating'' theorems for the TOV, whereby any given solution can be ``deformed'' to a new solution.
We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity equations are obtained quite directly.
We prove that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric and hence are all explicitly known.
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which contain shear. We obtain three different solutions out of these one turns out to be an incoherent dust solution and the other two are stiff matter solutions.
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding perfect fluid solutions possess finite/infinite extent. In the Newtonian case, for the large class of monotonic equations of state, and in General Relativity we improve earlier results.
I introduce a method to obtain the stress-energy tensor of the perfect fluid by adding a suitable term to the Einstein-Hilbert action. Variation should be understood with respect to the metric.
We present a method for generating exact diagonal $G_2$-cosmological solutions in dilaton gravity coupled to a radiation perfect fluid and with a cosmological potential of a special type. The method is based on the symmetry group of the system of $G_2$-field equations. Several new classes of explicit exact inhomogeneous perfect fluid scalar-tensor cosmologies are presented.
A global solution of the Einstein equations is given, consisting of a perfect fluid interior and a vacuum exterior. The rigidly rotating and incompressible perfect fluid is matched along the hypersurface of vanishing pressure with the stationary part of the Taub-NUT metric. The fluid core generates a negative-mass NUT space-time. The matching procedure leaves one parameter in the global solution.
A self-consistent system of interacting nonlinear spinor and scalar fields within the scope of a Bianchi type-I cosmological model filled with perfect fluid is considered. Exact self-consistent solutions to the corresponding field equations are obtained. The role of spinor field in the evolution of the Universe is studied. It is shown that the spinor field gives rise to an accelerated mode of expansion of the Universe. At the early stage of evolution the spinor field nonlinearity generates the acceleration while at the later stage it is done by the nonzero spinor mass.
Streamlines of a relativistic perfect isentropic fluid are geodesics of a Riemannian space whose metric is defined by enthalpy of the fluid. This fact simplifies the solution of some problems, as is also of interest from the point of view of fundamental physics.
We show that the analysis presented in a recent comment by Coll and Ferrando \cite{comment} (qr-qc/0312058) is based on the erroneous assumption that the chemical potential and fractional concentration of a {\it mixture} of perfect fluids are unknown variables.
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the metric stress-energy 4-form, the canonical energy-momentum 3-form and the hypermomentum 3-form) are obtained.
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the vacuum exterior which consists only of a stationary region of the Taub-NUT space-time. The solution of the matching conditions leaves generally three parameters in the global solution. Examples of perfect fluid sources are discussed.
In spite of a recent reply by Quevedo and Zárate (gr-qc/0403096), their assertion that their thermodynamic scheme for a perfect fluid binary mixture is incompatible with Szekeres and Stephani families of universes, except those of FRW ones, remains wrong.
Space-times admitting an $r$-parameter Lie group of homotheties are studied for $r > 2$ devoting a special attention to those representing perfect fluid solutions to Einstein's field equations.
It is proven that, under mild physical assumptions, an isolated stationary relativistic perfect fluid consists of a finite number of cells fibred by invariant annuli or invariant tori. For axially symmetric circular flows it is shown that the fluid consists of cells fibred by rigidly rotating annuli or tori.
We explore the symmetry group of the pressure isotropy condition in isotropic coordinates finding a rich structure. We work out some specific examples.
The article is devoted to cosmology. It deals with homogeneous anisotropic cosmological models. Scale factors have been evaluated for the multicomponent models with perfect fluid, taking account of its expansion, rotation and shear. The cosmological fluid components are as follows: phantom matter, de Sitter vacuum, domain walls, strings, dust, radiation, perfect gas, stiff matter and ekpyrotic matter. The scale factor dependences on the equation of state and kinematic invariants of the perfect fluid have been analysed. The paper is aimed at finding exact solutions of Friedmann and Raychaudhuri…
Self-consistent system of nonlinear spinor field and Bianchi I (BI) gravitational one with time dependent gravitational constant ($G$) and cosmological constant ($Λ$) has been studied. The initial and the asymptotic behaviors of the field functions and the metric one have been thoroughly investigated. Given $Λ= Λ_0/τ^2$, with $τ= \sqrt{-g}$, $G$ has been estimated as a function of $τ$. The role of perfect fluid at the initial state of expansion and asymptotical isotropization process of the initailly anisotropic universe has been elucidated.
In this short note we comment about some criticisms - appeared in a recent paper by Iguchi et al - to our previous works on gravitational collapse of perfect fluids. We show that those criticisms are incorrect on their own.
The gravitational field of a rigidly rotating perfect fluid cylinder with gamma- law equation of state is found analytically. The solution has two parameters and is physically realistic for gamma in the interval (1.41,2]. Closed timelike curves always appear at large distances.
A rigidly rotating incompressible perfect fluid solution of Einstein's gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the constant-pressure surfaces is positive and they have two ring-shaped cusps.
Within the scope of isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not possess nontrivial non-diagonal components of energy-momentum tensor, consequently does not impose any additional restrictions on the components of the spinor field or metric function. The spinor description of different matter was given and evolution of the Universe corresponding to these sources is illustrated. In the framework of a three fluid system the ut…
We recently showed (Class. Quantum Grav.\ 23, 3353; gr-qc/0602091) that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric (LRS) and hence are all explicitly known. We provide here a more transparent proof.
In this paper, we study in detail a perfect fluid cosmological model with time-varying "constants" using dimensional analysis and the symmetry method. We examine the case of variable "constants" in detail without considering the perfect fluid model as a limiting case of a model with a causal bulk viscous fluid as discussed in a recent paper. We obtain some new solutions through the Lie method and show that when matter creation is considered, these solutions are physically relevant.
General formulation of geometrization matter problem by scalar field $ϕ=\sqrt{-G_{55}}$ with the help of possibilities of classical 5-D Kaluza-Klein theory is given. Mathematical integrability conditions for such geometrization for the case of perfect fluid are derived.
We prove the existence of a class of perfect-fluid cosmologies with polarised Gowdy symmetry and a Kasner-like singularity. These solutions of the Einstein equations depend on four free functions of one space coordinate and are constructed by solving a system of Fuchsian equations.
We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.
We present a new non-diagonal G2 inhomogeneous perfect-fluid solution with barotropic equation of state p=rho and positive density everywhere. It satisfies the global hyperbolicity condition and has no curvature singularity anywhere. This solution is very simple in form and has two arbitrary constants.
By a weak deformation of the cylindrical symmetry of the potential vortex in a relativistic perfect isentropic fluid, we study the possible dynamics of the central line of this vortex. In "stiff" material the Nanbu-Goto equations are obtained
The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to $T^{μν}_{~~;μ}=λR^{,ν}$. In this work, we derive the Kerr-Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman-Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy ($ω=-2/3$) and the perfect fluid dark matter ($ω=-1/3$). Firstly, the Rastall parameter $κλ$ could be constrained by the weak energy condit…
Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known solutions are singled out from those obtained. The existence of the wormholes is proved.
We study `purely radiative' (div E = div H = 0) and geodesic perfect fluids with non-constant pressure and show that the Bianchi class A perfect fluids can be uniquely characterized --modulo the class of purely electric and (pseudo-)spherically symmetric universes-- as those models for which the magnetic and electric part of the Weyl tensor and the shear are simultaneously diagonalizable. For the case of constant pressure the same conclusion holds provided one also assumes that the fluid is irrotational.
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