Anisotropic strange stars in Tolman–Kuchowicz 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.     

Adler–Finch–Skea Anisotropic Solution in f ( $$\mathcal{G}$$ ) Gravity

In this paper, we develop anisotropic solution for spherically symmetric self-gravitating stellar object by employing Karmarkar embedding constraint in the framework of f($$\mathcal{G}$$) gravity. For this purpose, we use the mass and radius of three compact star models, i.e., Her X-1, SAX J 1808.4-3658, and 4U 1820-30 as well as smooth matching of spherical interior and Schwarzschild exterior spacetime geometries. The physical consistency and stability of the derived model is examined for these star models. We conclude that the resulting anisotropic model is physically viable as well as stable as it satisfies all the necessary requirements of the compact stellar objects.     

Double Degenerate Stars

Regardless of the formation mechanism, an exotic object, the double degenerate star (DDS), is introduced and investigated, which is composed of baryonic matter and some unknown fermion dark matter. Different from the simple white dwarfs (WDs), there is additional gravitational force provided by the unknown fermion component inside DDSs, which may strongly affect the structure and the stability of such kind of objects. Many possible and strange observational phenomena connecting with them are concisely discussed. Similar to the normal WD, this object can also experience thermonuclear explosion as type Ia supernova explosion when DDS's mass exceeds the maximum mass that can be supported by electron degeneracy pressure. However, since the total mass of baryonic matter can be much lower than that of WD at Chandrasekhar mass limit, the peak luminosity should be much dimmer than what we expect before, which may throw a slight shadow on the standard candle of SN Ia in the research of cosmology.     

A new model for strange stars

In the present work, we attempt to find a new class of solutions for the spherically symmetric perfect fluid sphere by employing the homotopy perturbation method (HPM), a new tool via which the mass polynomial function facilitates to tackle the Einstein field equations. A set of interior solutions found on the basis of the simplest MIT bag model equation of state in the form \(p=\frac{1}{3}(\rho -4B)\) where B is the bag constant. The proposed interior metric for the stellar system is consistent with the exterior Schwarzschild spacetime on the boundary. In addition, we also conduct a detailed study on different tests, viz. the energy conditions, TOV equation, adiabatic index, Buchdahl limit, etc., to verify the physical validity of the proposed model. The numerical value of the used parameters are predicted for different strange star candidates, for different chosen values of the bag constant. In a nutshell, by exploiting HPM technique first time ever in the field of relativistic astrophysics, we have predicted in the present literature a singularity-free and stable stellar model which is suitable to describe ultra-dense objects, like strange (quark) stars.     

An Exact Family of Einstein–Maxwell Wyman–Adler Solution in General Relativity

This paper presents a family of two-parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with particular choice of charge distribution and the metric component g ₀₀. This family gives us wide range of parameters, n and K, for which the solutions are regular and acceptable on physical grounds and hence suitable for modeling of charged compact star. The maximum allowable mass and corresponding radius, for this family of solutions with the particular form of charge distribution, is determined to be 2.48M _⊙ and 10.56 km respectively by assuming the stellar “surface” density equal to strange (quark) matter density at zero pressure. It is hoped that our investigation may be of some importance in connection with the study of internal structure of electrically charged strange (quark) star.     

Mathematical Model of Relativistic Anisotropic Compact Stellar Model Admitting Linear Equation of State

In present paper, a static, spherically symmetric, anisotropic stellar object has been discussed by assuming a linear relationship between the matter density ρ and radial pressure pr. The interior solution is continuously matched with the exterior Schwarzschild vacuum solution at the junction interface. Various physical features viz. energy conditions, mass-radius relationship, stability are analyzed for our stellar model. By assigning some particular value to the arbitrary constants we have obtained a model of compact star of radius 6.7 km. and mass 1.148 M⊙, which is very close to the observational data of the compact star Her X-1 proposed by Rawls et al.[Rawls, et al., Astrophys. J. 730 (2011) 25]. We have obtained that the model satisfies all the regularity conditions. We have found that our proposed model is stable as well as singularity-free.     

有限温度下的二维暗能量星模型

研究了具有奇异物质作用的二维暗能量星模型,推导出了场方程和星体平衡方程;并获得了一些解析解,计算出了星体质量.另外,还研究了温度对星体质量的影响,发现几种情况下星体总质量都具有上限. 关键词： 暗能量星 奇异物质 有限温度     

All possible tripartitions of $${}^{}$$U isotope in collinear configuration

In this work we provide a framework for modelling compact stars in which the interior matter distribution obeys a generalised Chaplygin equation of state. The interior geometry of the stellar object is described by a spherically symmetric line element which is simultaneously co-moving and isotropic with the exterior space–time being vacuum. We are able to integrate the Einstein field equations and present closed form solutions which adequately describe compact strange star candidates such as 4U 1538-52, PSR J1614-2230, Vela X-1 and Cen X-3 (Gangopadhyay et al, Mon. Not. R. Astron. Soc. 431, 3216 (2013)).     

Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

The exact solution for the electromagnetic field occuring when the Kerr–Taub–NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr–Taub–NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of the central gravitating object. Finally we find analytical solutions of Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star. The star is considered isolated and in vacuum, with monopolar configuration model for the stellar magnetic field.     

密度依赖口袋常数下奇异物质的热力学自洽处理及其对混合星性质的影响

在MTT口袋模型的基础上采用密度依赖口袋常数,给出了奇异夸克物质的热力学关系,并用于描述奇异夸克物质及混合星内的夸克相,研究了奇异星、混合星的性质.结果表明,密度依赖口袋常数下,奇异夸克物质的压强公式中有一个附加项,而能量密度中则没有,从而保证了系统的热力学自洽性.在新的热力学关系下,奇异夸克物质的状态方程变软,相应的奇异星的引力质量和对应的半径均变小;混合星的状态方程也变软,其质量变小,而对应的半径也变小.说明经热力学自洽处理后该模型对中子星的状态方程及相应的质量-半径关系等都有显著的影响.     

On relativistic models of strange stars

The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein’s field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.      

Dark matter, neutron stars, and strange quark matter

We show that self-annihilating weakly interacting massive particle (WIMP) dark matter accreted onto neutron stars may provide a mechanism to seed compact objects with long-lived lumps of strange quark matter, or strangelets, for WIMP masses above a few GeV. This effect may trigger a conversion of most of the star into a strange star. We use an energy estimate for the long-lived strangelet based on the Fermi-gas model combined with the MIT bag model to set a new limit on the possible values of the WIMP mass that can be especially relevant for subdominant species of massive neutralinos.     

Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) 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.     

Estimate of stellar masses from their QPO frequencies

Kilohertz quasiperiodic oscillations (kHz QPOs) are observed in binary stellar systems. For such a system, the stellar radius is very close to the marginally stable orbit R _ms as predicted by Einstein’s general relativity. Many models have been proposed to explain the origin of the kHz QPO features in the binaries. Here we start from the work of Li et al (Phys. Rev . Lett. 83, 3776 (1999)) who in 1999, from the unique millisecond X-ray pulsations, suggested SAX J1808.4−3658 to be a strange star, from an accurate determination of its rotation period. It showed kHz QPOs eight years ago and so far it is the only set that has been observed. We suggest that the mass of four compact stars SAX J1808.4−3658, KS 1731−260, SAX J1750.8−2900 and IGR J17191−2821 can be determined from the difference in the observed kHz QPOs of these stars. It is exciting to be able to give an estimate of the mass of the star and three other compact stars in low-mass X-ray binaries using their observed kHz QPOs.     

奇异星的冷却

从奇异夸克物质的热力学巨势出发计算了奇异星的组份，得到电子丰度随强相互作用耦合常数或奇异物质的密度增大而减小．利用弱电统一理论，推导了奇异物质的中微子能量损失率。通过研究有薄壳的均匀奇异星和中子垦的冷却过程，得到年轻奇异星的表面温度比同年代的中子星的表面温度低得多，这可以作为区别奇异星与中子星的观测途径。 关键词：     

A class of exact strange quark star model

Static spherically symmetric space-time is studied to describe dense compact star with quark matter within the framework of MIT Bag Model. The system of Einstein’s field equations for anisotropic matter is expressed as a new system of differential equations using transformations and it is solved for a particular general form of gravitational potential with parameters. For a particular parameter, as an example, it is shown that the model satisfies all major physical features expected in a realistic star. The generated model also smoothly matches with the Schwarzschild exterior metric at the boundary of the star. It is shown that the generated solutions are useful to model strange quark stars.     

Dense stars with exotic configurations

In this paper, we consider dense stars with configurations expected from the SU(3)_C×SU(2)_W× U(1) standard model of strong and electroweak interactions. Following a recent suggestion that strange matter, a form of (uds) quark matter, may be the true ground state of hadronic matter, we investigate the prospect for the existence of dense stars consisting partially, or entirely, of strange matter by comparing the relative stability between neutron matter and strange matter. It is found that the restriction on the maximum star mass holds in all cases, including a pure strange star, a pure neutron star, and a neutron star with a quark core. It is also found that the choice of both the bag constantB and the strong coupling constant _s has a decisive effect on the relative stability between strange matter and neutron matter. For currently accepted values of (B, _s), anA= dense starcannot consist entirely,nor partially, of strange matter. Nevertheless, such conclusion may be subject to change if corrections ofO ( _s ² ) or other effects are taken into account. Finally, we use the framework of Tolman, Oppenheimer, and Volkoff to analyze two cases of boson stars: gluon stars and stars consisting of massive scalar particles (massive bosons). It is found that, in the case of gluon stars, the presence of the bag constant in the QCD vacuum yields results very similar to that found in quark stars. On the other hand, soliton stars consisting of massive bosons exist if there is some background pressure which plays the role similar to the bag constant for lowering the matter pressure. The stability problem for both gluon stars and soliton stars is briefly discussed.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Extended gravitational decoupled charged anisotropic solutions

In this paper, we study exact charged anisotropic spherical solutions through extended geometric deformation technique. For this purpose, we consider the singularity-free Krori–Barua solution and extend it to attain two analytical anisotropic models in the presence of the electromagnetic field. We examine energy bounds as well as causality condition for the star Her X-I to analyze the viability of the obtained solutions. It is found that both models show realistic behavior as they satisfy all physical constraints as well as stability criterion. We conclude that the extended gravitational decoupling approach provides more stable results for the stellar system in contrast to minimal geometric deformation.     

Lower limit on radius as a function of mass for neutron stars

A model-independent limit on neutron star radius as a function of mass based only on well-accepted principles is derived. We discuss our limit in connection with a recent interpretation of x-ray pulsations from SAX J1808.4-3658 as indicating a strange-star candidate, and show that this object can also be a normal neutron star, though one whose central core has very high density. The most plausible high-density phase of hadronic matter, which is also expected to be very compressible, is quark matter. So an alternative to the strange star interpretation of SAX J1808.4-3658 is that it is a hybrid neutron star.