New classes of anisotropic models with generalized polytropic equation of state

In this paper, we investigate the gravitational behavior of compact objects with the help of generalized polytropic equation of state in isotropic coordinates. We found three exact solutions of Einstein field equations by taking into account the different values of polytropic index with spherically symmetric anisotropic inner fluid distribution. We have regained the masses of PSR \(\hbox {J}1614-2230\), Vela X-1, Vela 4U, PSR J1903+327 and 4U 1820-30. Speed of sound has been used to analyze the stability of models. The comprehensive analysis indicates that all the models are physically viable and well behaved.     

Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane–Emden type

Lane–Emden equation is a nonlinear singular equation in the astrophysics that corresponds to the polytropic models. In this paper, a pseudospectral technique is proposed to solve the Lane–Emden type equations on a semi-infinite domain. The method is based on rational Legendre functions and Gauss–Radau integration. The method reduces solving the nonlinear ordinary differential equation to solve a system of nonlinear algebraic equations. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method.     

Natures of Statefinder Parameters and Om Diagnostic for Cardassian Universe in Ho?ava-Lifshitz Gravity

In this work, we have considered Cardassian Universe in Ho?ava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Ho?ava-Lifshitz gravity.     

Accretion onto a Kiselev black hole

We consider accretion onto a Kiselev black hole. We obtain the fundamental equations for accretion without the back-reaction. We determine the general analytic expressions for the critical points and the mass accretion rate and find the physical conditions the critical points should fulfill. The case of a polytropic gas are discussed in detail. It turns out that the quintessence parameter plays an important role in the accretion process.     

Cosmological Constraints on Polytropic Gas Model

We study the polytropic gas scenario as the unification of dark matter and dark energy. We fit the model parameters by using the latest observational data including type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble parameter data. At 68.3 % and 95.4 % confidence levels, we find the best fit values of the model parameters as $\tilde{K}=0.742_{-0.024}^{+0.024}(1\sigma)_{-0.049}^{+0.048}(2\sigma)$ and $n=-1.05_{-0.08}^{+0.08}(1\sigma)_{-0.16}^{+0.15}(2\sigma)$ . Using the best fit values of the model, we obtain the evolutionary behaviors of the equation of state parameters of the polytropic gas model and dark energy, the deceleration parameter of the universe, the dimensionless density parameters of dark matter and dark energy as well as the growth factor of structure formation. Then, we investigate different energy conditions in the polytropic gas model and obtain that only the strong energy condition is violated for the special ranges of the redshift. We also conclude that in the this model, the universe starts from the matter dominated epoch and approaches a de Sitter phase at late times, as expected. Further, the universe begins to accelerate at redshift z _t=0.74. Furthermore, in contrary to the ΛCDM model, the cosmic coincidence problem is solved naturally in the polytropic gas scenario. Moreover, this model fits the data of the growth factor well as the ΛCDM model.     

Newtonian stellar models

We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a three-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two two-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Moreover, it makes a host of mathematical tools from dynamical systems theory available, which allows us to prove several theorems about the relationship between the equation of state and properties concerning total masses and radii.     

Electromagnetic effects on complexity factor for static cylindrical system

This paper investigates the phenomenon of complexity factor for static charged anisotropic cylindrical configuration. We formulate some basic equations such as Einstein–Maxwell field equations, Tolman–Opphenheimer–Volkoff equation and mass equation. Further, the orthogonal splitting of the Riemann tensor is used to obtain the structure scalars that lead to the complexity factor. Finally, we investigate some theoretical models with vanishing complexity condition. It is found that the complexity of the system increases for α ≤ 1 in the presence of the electromagnetic field.     

Reissner–Nordström and Charged Gas Spheres

This paper studies polytropic gas spheres with some innovations. The main idea, already advanced in the context of neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is that the mass distribution extends to infinity, the boundary between bulk and atmosphere being defined by an abrupt change in the polytropic index, triggered by the density. The logical next step is to include the effect of radiation, which is a very significant complication since a full treatment would have to include an account of ionization, thus fields representing electrons, ions, photons, gravitons and neutral atoms as well. In way of preparation, we consider models that are charged but homogeneous, involving only gravity, electromagnetism and a single scalar field that represents both the mass and the electric charge; in short, a non-neutral plasma. While this work only represents a stage in the development of a theory of stars, without direct application to physical systems, it does shed some light on the meaning of the Reissner–Nordström solution of the modified Einstein–Maxwell equations. But the main point of the paper is a suggestion about the proper place of the photon gas in a theory of stellar structure and other plasmas, with an application to a simple system; it is proposed to treat the photon gas as part of the dynamics.     

Interacting polytropic gas model of phantom dark energy in?non-flat universe

By introducing the polytropic gas model of interacting dark energy, we obtain the equation of state for the polytropic gas energy density in a non-flat universe. We show that for an even polytropic index by choosing $K>Ba^{\frac{3}{n}}$K>Ba^{\frac{3}{n}} , one can obtain ω _Λ ^eff<−1, which corresponds to a universe dominated by phantom dark energy.     

Some charged polytropic models

The Einstein–Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43:1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44:1419, 2012) are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars.     

Patterns of diffractive production

We discuss diffractive production in the context of two-component models. After defining the class of models that we consider and discussing their general properties, we develop integral equations for the generating functions of diffractive processes. We consider single and double diffraction and two fireball production. We investigate the behavior of the partial cross sections for n-particle production in all three cases and obtain a successful fit to recent data.     

Velocity and velocity bounds in static spherically symmetric metrics

We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.     

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean-field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involving a damping term. In the limit of small frictions, we obtain a hyperbolic model describing the formation of network patterns (filaments) and in the limit of strong frictions we obtain a parabolic model which is a generalization of the standard Keller-Segel model describing the formation of clusters (clumps). Our approach connects and generalizes several models introduced in the chemotactic literature. We discuss the analogy between bacterial colonies and self-gravitating systems and between the chemotactic collapse and the gravitational collapse (Jeans instability). We also show that the basic equations of chemotaxis are similar to nonlinear mean-field Fokker-Planck equations so that a notion of effective generalized thermodynamics can be developed.     

Analysis of the Bethe ansatz equations of the XXZ model

We analyse the Bethe ansatz equations of the XXZ model in the antiferromagnetic region, without assuming a priori the existence of strings. Excited states are described by a finite number of parameters. These parameters satisfy a closed system of equations, which we obtain by eliminating the parameters of the vacuum from the original Bethe ansatz equations. Strings are only particular solutions of these equations.     

Dynamical Evolution and Leading Order Gravitational Wave Emission of Riemann-S Binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index n, on the leading order gravitational waveforms is studied.     

Integrable geodesic flows and super polytropic gas equations

The polytropic gas equations are shown to be the geodesic flows with respect to an L² metric on the semidirect product space Diff(S¹)C^∞(S¹), where Diff(S¹) is the group of orientation preserving diffeomorphisms of the circle. We also show that the N=1 supersymmetric polytropic gas equation constitute an integrable geodesic flow on the extended Neveu–Schwarz space. Recently other kinds of supersymmetrizations have been studied vigorously in connection with superstring theory and are called supersymmetric-B (SUSY-B) extension. In this paper we also show that the SUSY-B extension of the polytropic gas equation form a geodesic flow on the extension of the Neveu–Schwarz space.     

Cosmological Implications of Interacting Polytropic Gas Dark Energy Model in Non-flat Universe

The polytropic gas model is investigated as an interacting dark energy scenario. The cosmological implications of the model including the evolution of EoS parameter w _Λ, energy density Ω_Λ and deceleration parameter q are investigated. We show that, depending on the parameter of model, the interacting polytropic gas can behave as a quintessence or phantom dark energy. In this model, the phantom divide is crossed from below to up. The evolution of q in the context of polytropic gas dark energy model represents the decelerated phase at the early time and accelerated phase later. The singularity of this model is also discussed. Eventually, we establish the correspondence between interacting polytropic gas model with tachyon, K-essence and dilaton scalar fields. The potential and the dynamics of these scalar field models are reconstructed according to the evolution of interacting polytropic gas.     

On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations

We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter τ > 0 and 2nd order space and time derivatives; the body force is taken into account. We transform it to a form close to the compressible Navier–Stokes system of equations. Then we derive the entropy balance equation and show that the entropy production is similar to the latter system plus a term of the order of O(τ²). We analyze an equation for the total entropy as well. We also show that the corresponding residuals in the HQGD equations with respect to the compressible Navier–Stokes ones are of the order of O(τ²) too. Finally we treat the simplified barotropic HQGD system of equations with the general state equation and the stationary potential body force and obtain the corresponding results for it.     

Palatini formulation of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity theory,and its cosmological implications

We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type \(f=R-\alpha ^2/R+g(T)\) and \(f=R+\alpha ^2R^2+g(T)\) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.