Symmetric Star Research Articles

Anisotropic fluid spheres satisfying the Karmarkar condition

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M[Formula: see text], R = 9.56 km) and Cen X-3 (Mass = 1.49 M[Formula: see text], R = 9.17 km).

On the inverse spectrum problem of neutron stars

In this work we revisit axial perturbations of spherically symmetric and non-rotating neutron stars. Although it has been object of many studies, it still offers new insights that are of potential interest for more realistic scenarios or in the study exotic compact objects, which have drawn much attention recently. By using WKB theory, we first derive a new Bohr–Sommerfeld rule that allows to investigate the quasi-normal mode spectrum and address the inverse spectrum problem. The pure analytical treatment of the wave equation is rather involved, because it requires the solution of the TOV equations and the non-trivial tortoise coordinate transformation depending on the underlying space-time. Therefore we provide an easy way to construct potentials that simplifies the analytical treatment, but still captures the relevant physics. The approximated potential can be used for calculations of the axial perturbation spectrum. These results are also useful in the treatment of the inverse problem. We demonstrate this by reconstructing the time–time component of the metric throughout the star and constraining the equation of state in the central region. Our method also provides an analytical explanation of the empirically known asteroseismology relation that connects the fundamental QNM and radius of a neutron star with its compactness.

The Dual Blaschke Addition

It is remarkable that there is a duality in geometric tomography between results on projections of convex bodies and results on sections of star (rather than convex) bodies. The radial Blaschke addition, which is the dual version of Blaschke addition, as an operation between central symmetric star bodies is introduced in this paper. The relationship between it and the classical radial addition, many properties of radial Blaschke addition and related inequalities are established.

Stochastic metric perturbations (radial) in gravitationally collapsing spherically symmetric relativistic star

Stochastic perturbations (radial) of a spherically symmetric relativistic star, modeled by a perfect fluid in comoving coordinates for the collapse scenario are worked out using the classical Einstein- Langevin equation, which has been proposed recently. The solutions are in terms of perturbed metric potentials and their two point correlation. For the case worked out here, it is interesting to note that the two perturbed metric potentials have same magnitude, while the potentials themselves are in general independent of each other. Such a treatment is useful for building up basic theory of non-equilibrium and near equilibrium statistical physics for collapsing stars, which should be of interest towards the end states of collapse. Here we discuss the first simple model, that of non-rotating spherically symmetric dynamically collapsing relativistic star. This paves way to further research on rotating collapse models of isolated as well as binary configurations on similar lines . Both the radial and non-radial perturbations with stochastic effects would be of interest to asteroseismology, which encompassed the future plan of study.

Boson star from repulsive light scalars and gravitational waves

We study properties of boson stars consisting of ultra-light scalar dark matter with repulsive self-interactions. We investigate the origin of the maximum mass of spherically symmetric stable stars which emerges only when solving the full equations of motion in curved space-time, but not when solving the approximated Schrödinger-Newton equations. When the repulsion is weak, the backreaction of the curvature on the scalars acts as an additional source of attraction and can overcome the repulsion, resulting in a maximum star mass and compactness. We also point out that the potential in a UV completed particle physics model of light scalar dark matter is generally more complicated than the widely used ϕ4 interaction. Additional interactions beyond ϕ4 in the potential can dramatically change the properties of boson stars as well as modify the prospect of LIGO gravitational wave detection for binary mergers of boson stars.

No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions

We study scalar condensation in the background of asymptotically flat spherically symmetric regular Dirichlet stars. We assume that the scalar field decreases as the star surface is approached. Under these circumstances, we prove a no hair theorem for neutral regular compact stars. We also extend the discussion to charged regular compact stars and find an upper bound for the charged star radius. Above the upper bound, the scalar hair cannot exist. Below the upper bound, we numerically obtain solutions of scalar hairy charged stars.

Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks.

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual “slip-links”, each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight , a key tube theory parameter, can be extracted. The procured value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms , or equivalently arm end-to-end vector relaxation function , through the mean FP time spectrum of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation.

Anisotropic compact stars in the Buchdahl model: A comprehensive study

In this article, we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized matric potential, namely, Buchdahl ansatz [Phys. Rev. D \textbf{116}, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein field equations(EFEs) with a perfect fluid source, including in particular the Vaidya-Tikekar and Finch-Skea. We here developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that plays a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$, and analyzed them in a uniform manner. As a result, it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the framework of the anisotropic hypothesis, we consider analogue objects with similar mass and radii such as LMC X-4, SMC X-1, EXO 1785-248 \emph{etc} to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P = P (\rho)$, we demonstrate that EoSs can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

Multichain Slip-Spring Simulations for Branch Polymers

Although the tube models have attained remarkable success, development of a simulation method for entangled branch polymer dynamics is still a challenge. In this study, the multichain slip-spring model has been examined to branch polymers for the first time. In the model, the bead–spring chains are dispersed in the simulation box, and the entanglement is mimicked by the virtual spring, so-called slip-spring, which connects the chains and hops along the chain. The slip-springs are created and destructed only at the chain ends. Besides, for the relaxation of entanglements formed between the backbone chains in the branch polymers, the hopping of the slip-spring across the branch point (SHAB) is additionally allowed when the branching arm relaxes. The simulation results for symmetric and asymmetric star and H branch polymers are in semiquantitative agreement with experimental and earlier simulation data extracted from the literature. Although the proposed simulation is compatible with the data for scarcely en...

From dinuclear systems to close binary stars: Application to source of energy in the universe

The evolution of close binary stars in mass asymmetry (transfer) coordinate is considered. The conditions for the formation of stable symmetric binary stars are analyzed. The role of symmetrization of asymmetric binary star in the transformation of potential energy into internal energy of star and the release of a large amount of energy is revealed.

Atmospheres and wind properties of non-spherical AGB stars

Context. The wind-driving mechanism of asymptotic giant branch (AGB) stars is commonly attributed to a two-step process: first, gas in the stellar atmosphere is levitated by shockwaves caused by stellar pulsation, then accelerated outwards by radiative pressure on newly formed dust, inducing a wind. Dynamical modelling of such winds usually assumes a spherically symmetric star. Aims. We explore the potential consequences of complex stellar surface structures, as predicted by three-dimensional (3D) star-in-a-box modelling of M-type AGB stars, on the resulting wind properties with the aim to improve the current wind models. Methods. Two different modelling approaches are used; the CO5BOLD 3D star-in-a-box code to simulate the convective, pulsating interior and lower atmosphere of the star, and the DARWIN one-dimensional (1D) code to describe the dynamical atmosphere where the wind is accelerated. The gas dynamics of the inner atmosphere region at distances of R ∼ 1−2 R⋆, which both modelling approaches simulate, are compared. Dynamical properties and luminosity variations derived from CO5BOLD interior models are used as input for the inner boundary in DARWIN wind models in order to emulate the effects of giant convection cells and pulsation, and explore their influence on the dynamical properties. Results. The CO5BOLD models are inherently anisotropic, with non-uniform shock fronts and varying luminosity amplitudes, in contrast to the spherically symmetrical DARWIN wind models. DARWIN wind models with CO5BOLD-derived inner boundary conditions produced wind velocities and mass-loss rates comparable to the standard DARWIN models, however the winds show large density variations on time-scales of 10–20 yr. Conclusions. The method outlined in this paper derives pulsation properties from the 3D star-in-a-box CO5BOLD models, to be used in the DARWIN models. If the current grid of CO5BOLD models is extended, it will be possible to construct extensive DARWIN grids with inner boundary conditions derived from 3D interior modelling of convection and pulsation, and avoid the free parameters of the current approach.

Comment on “Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case”

Recently, the covariant formulation of the Tolman-Oppenheimer-Volkoff (TOV) equations for studying the equilibrium structure of a spherically symmetric compact star in the presence of the pressure anisotropy in the interior of a star was presented in Phys. Rev. D \textbf{97} (2018) 124057. It was suggested there that the anisotropic solution of these equations can be obtained by finding, first, the solution of the common TOV equations for the isotropic pressure, and then by solving the differential equation for the anisotropic pressure whose particular form was established on the basis of the covariant TOV equations. It turns out that the anisotropic pressure determined according to this scheme has a nonremovable singularity $\Pi\sim\frac{1}{r^2}$ in the center of a star, and, hence, the corresponding anisotropic solution cannot represent a physically relevant model of an anisotropic compact star. A new scheme for constructing the anisotropic solution, based on the covariant TOV equations, is suggested, which leads to the regularly behaved physical quantities in the interior of a star. A new algorithm is applied to build model anisotropic strange quark stars with the MIT bag model equation of state.

Coarse-Grained Simulations of Three-Armed Star Polymer Melts and Comparison with Linear Chains.

Melts of three-armed star polymers have been simulated using a coarse-grained model parameterized by atomistic simulations of polyethylene. The bonds between the highly coarse-grained, and hence soft, polymer beads are explicitly prevented from crossing by the TWENTANGLEMENT algorithm. The three melts of symmetric stars, differing in the lengths of the arms, are compared against five melts of linear polymers with comparable dimensions to study the impact of branched architecture on self-diffusion and bulk rheological properties. Differently from the power-law relation between the viscosity and molecular mass of linear chains, the star polymers in our simulations follow an exponential mass-viscosity relation and show qualitative agreement with the storage and loss moduli for stars with far longer arms from experiments. The stress relaxation dynamics of the stars are also compared with theoretical analysis in terms of Rouse modes.

Anisotropic quark stars in f(R,\xa0T) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.

-boson stars

We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein–Klein–Gordon system for a collection of an arbitrary odd number N of complex scalar fields with an internal symmetry and no self-interactions. These solutions, which we dub -boson stars, are parametrized by an angular momentum number , an excitation number n, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For the standard spherically symmetric boson stars are recovered. We determine their generalizations for , and show that they give rise to a large class of new static configurations which might have a much larger compactness ratio than stars.

Spontaneous growth of spinor fields in gravity

We show that spinor fields nonminimally coupled to gravity can grow spontaneously in the presence of matter. We name this phenomenon spontaneous spinorization after the spontaneous scalarization scenario in scalar-tensor theories. Underlying reason for the growth of the spinor is an instability similar to the tachyon of spontaneous scalarization. We first present the structure of a tachyonic Dirac equation, and incorporate it into the matter coupling in gravity. This causes the zero-spinor solution to be unstable and leads to spontaneous growth. We investigate the behavior of the resulting theory for a spherically symmetric neutron star that has grown a spinor cloud. Spontaneous spinorization has the potential to lead to order-of-unity deviations from general relativity in strong fields in a similar manner to its close relative spontaneous scalarization. This makes the theory especially relevant to gravitational wave science and neutron star astrophysics.

Compact stars in energy-momentum squared gravity

A simple generalization to Einstein's general relativity (GR) was recently proposed which allows a correction term $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory. This theory is called Energy-Momentum Squared Gravity (EMSG) and introduces a new coupling parameter $\eta$. EMSG resolves the big bang singularity and has a viable sequence of cosmological epochs in its thermal history. {Interestingly, in the vacuum EMSG is equivalent to GR, and its effects appear only inside the matter-energy distribution. More specifically, its consequences appear in high curvature regime. Therefore it is natural to expect deviations form GR inside compact stars. In order to study spherically symmetric compact stars in EMSG, we find the relativistic governing equations. More specifically, we find the generalized version of the Tolman-Oppenheimer-Volkov equation in EMSG. Finally we present two analytical solutions, and two numerical solutions for the field equations. For obtaining the numerical solutions we use polytropic equation of state which is widely used to understand the internal structure of neutron stars in the literature. Eventually we find a mass-radius relation for neutron stars. Also, We found that EMSG, depending on the central pressure of the star and the magnitude of free parameter $\eta$, can lead to larger or smaller masses for neutron stars compared with GR. Existence of high-mass neutron stars with ordinary polytropic equation of state in EMSG is important in the sense that these stars exist in GR provided that one use exotic equation of states.

Anisotropic strange stars in Tolman\u2013Kuchowicz spacetime

We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einstein’s general theory of relativity by exploiting the Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) metric. Further, we have assumed that the cosmological constant varLambda is a scalar variable dependent on the spatial coordinate r. To describe the strange star candidates we have considered that they are made of strange quark matter distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman–Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. (Ann Phys 387:239, 2017) we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the varLambda as well as the bag constant {mathcal {B}}. The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the varLambda and {mathcal {B}} increase the anisotropic system become gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.

From dinuclear systems to close binary stars: Application to mass transfer

Applying the microscopic nuclear physics ideas to macroscopic stellar systems, we study the evolution of the compact di-stars in mass asymmetry (transfer) coordinate. Depending on the internal structure of constituent stars, the initial mass asymmetry, total mass, and orbital angular momentum, the close di-star system can either exist in symmetric configuration or fuse into mono-star. The limitations for the formation of stable symmetric binary stars are analyzed.

Stable anisotropic dissipative quark star with tilted observer

This paper is aimed to study spherically symmetric anisotropic dissipative quark star for tilted observer. The corresponding field equations as well as dynamical equations are formulated. We consider the MIT bag model for quark stars and investigate numerical solution of the field equations by imposing the shear-free condition. It is found that all the expected physical properties are present related to stellar fluid distribution. Finally, we analyze stability of the compact object by analyzing splitting of the fluid distribution. It is found that radial velocity does not change its sign during evolution of the system implying that the system does not undergo splitting and remains stable.