Superdense Stars Research Articles

Relativistic stellar modeling with perfect fluid core and anisotropic envelope fluid

We investigate the effect of density perturbations and local anisotropy on the stability of stellar matter structures in general relativity using the concept of cracking. Adopting a core-envelope model of a super-dense star, we examine the properties and stability conditions by introducing anisotropic pressure to the envelope region. Furthermore, we propose self-bound compact stars with an anisotropic envelope as a potential progenitor for starquakes. We show how the difference between sound propagation in radial and tangential directions would be used to identify potentially stable regions within a configuration. Due to an increase in the anisotropic parameter, strain energy accumulates in the envelope region and becomes a potential candidate for building-up quake like situation. This stress-energy stored in the envelope region that would be released during a starquake of a self-bound compact star is computed as a function of the magnitude of anisotropy at the core-envelope boundary. Numerical studies for spherically asymmetric compact stars indicate that the stress energy can be as high as $$10^{50}$$ erg if the tangential pressure is slightly more significant than the radial pressure. It is happened to be of the same order as the energy associated with giant $$\gamma $$ -ray bursts. Thus, the present study will be useful for the correlation studies between starquakes and GRBs.

A viable relativistic charged model of super-dense star LMC X-4

In this work, we present an exact interior solution to a physically acceptable Einstein–Maxwell equation system, assuming a static and spherically symmetric spacetime with a distribution of matter from a perfect charged fluid to represent a generalization of a model for a perfect chargeless fluid. The charge parameter modifies the mass function, its compactness rate and the comportment of the speed of sound. The behavior analysis of the functions of density, pressure and charge shows that the solution is applicable for the description of relativistic compact stars. In particular, we analyze the behavior of these functions for the values of observed mass [Formula: see text] and the theoretical radius interval estimated previously [Formula: see text][Formula: see text]km from the star LMC X-4. Thus, the biggest charge value of maximum charge [Formula: see text]C occurs for the maximum compactness [Formula: see text].

Relativistic models of anisotropic superdense star in the regime of Karmarkar’s condition

We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding condition. To obtain the closed-form solution a suitable form of one of the gravitational potentials has been chosen to determine the other by analyzing the Karmarkar condition. The resulting solutions are found to be well-behaved and regular and could describe a compact stellar object. Considering the current estimated values of the mass and radius of the pulsar 4U1820 − 30 as input parameters, all the physically relevant parameters are shown to be well-behaved to a very good degree of accuracy.

Three-layered super dense star with charged anisotropic fluid

We generate a three-layered super dense charged star with Van der Waals equation of state at the intermediate layer of stellar spheres. Our model comprises of three interior layers: the core, the intermediate, and the envelope described by linear, Van der Waals, and Chaplygin equations of state, respectively. The plots for the physical variables such as energy density, radial and tangential pressures, mass, anisotropy, and metric potentials are well behaved and agree with the astrophysical results. The stability and equilibrium factors are continuous and defined at some values of the parameters. We have also generated new stellar masses and radii which are in acceptable ranges. We have also regained previous masses and radii for the stars like PSRJ1903+0327, PSRJ1614-2230, SAXJ1808.4-3658, EXO1745-248, and EXO1785-248.

Anisotropic model of super dense star with linearized core and Van der Waals envelope

In this research, core envelope model of a super dense spherically symmetric compact star is developed by considering anisotropic matter configuration. The core is represented by a linear equation of state (EOS), whereas the Van der Waals EOS is used in the envelope region. In the core and envelope of the star, all geometrical and physical factors are viable. The three regions, i.e. the core, envelope and outer space satisfy the junction conditions. The proposed model validates with the properties of Vela X-1, Her X-1 and SMC X-1. It is concluded that in the model presented, the core of the star compresses as the mass increases justifying the domination of gravitational effects on massive astronomical objects.

A new class of charged spherically symmetric and static superdense star configurations

In this paper, we have obtained a new family of interior solutions of the Einstein–Maxwell field equations in general relativity for static, spherically symmetric distribution of charged fluid. The electric density is assumed to be [Formula: see text] where [Formula: see text] is a positive constant. The solution is well behaved for a wide range of [Formula: see text] hence, it is suitable for modeling a superdense star. The surface density is assumed to be [Formula: see text], for the validation of the solution set present, a comparison has also been made with the stars EXO 1785-248, SMC X-1, Her X-1, 4U 1538-52. For these particular stars, the maximum value of surface redshift is obtained to be 0.3251 for the star EXO 1785-248 and the minimum value is obtained as 0.2027 for the star Her X-1. We subject our solution to rigorous physical viability tests. In the absence of charge, we obtain the regular and well-behaved sixth model of Durgapal.

STATIC GENERAL SOLUTION TO EINSTEIN’S FIELD EQUATIONS

We consider the Vaidya Tikekar metric; 3- dimensional space with time (t) being constant, in a super dense star which is spheroidal. We report a static general solution (in terms of hyper-geometric series) to Einstein's field equations using Vaidya-Tikekar metric.

New exact even-dimensional pure Lovelock interior metrics

While it is well known that Nth-order pure Lovelock spacetimes of dimension $$d = 2N + 1$$ do not admit bounded compact objects, this is not the case for the $$d = 2N + 2$$ case. In the $$N = 2$$ , pure Gauss–Bonnet gravity exact models for the Vaidya–Tikekar superdense star ansatz are investigated and new classes of metrics are discovered in terms of elementary functions. An astrophysical model of a stellar distribution that is consistent with the physical expectations extrapolated from four-dimensional gravity is exhibited. The isothermal sphere is re-considered and found to be inconsistent in pure Lovelock theory. Finally, we briefly consider the case of the third-order Lovelock polynomial term and several classes of exact solutions emerge.

Distinct classes of compact stars based on geometrically deduced equations of state

We have computed the properties of compact objects like neutron stars based on equation of state (EOS) deduced from a core–envelope model of superdense stars. Such superdense stars have been studied by solving Einstein’s equation based on pseudo-spheroidal and spherically symmetric spacetime geometry. The computed star properties are compared with those obtained based on nuclear matter EOSs. From the mass–radius ([Formula: see text]–[Formula: see text]) relationship obtained here, we are able to classify compact stars in three categories: (i) highly compact self-bound stars that represents exotic matter compositions with radius lying below 9[Formula: see text]km; (ii) normal neutron stars with radius between 9 to 12[Formula: see text]km and (iii) soft matter neutron stars having radius lying between 12 to 20[Formula: see text]km. Other properties such as Keplerian frequency, surface gravity and surface gravitational redshift are also computed for all the three types. This work would be useful for the study of highly compact neutron like stars having exotic matter compositions.

Perfect fluid filled universe in odd dimensional pure Lovelock gravity

It is well known that d = 2 N + 1 dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that 2 N + 1 pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with d = 2 N + 1 that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ( N = 2 ) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all N and d = 2 N + 1 . In particular the special case N = 3 , d = 7 has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.

Relativistic compact stars in the Kuchowicz space-time

We present an anisotropic charged analogue of Kuchowicz (1971) solution of the general relativistic field equations in curvature coordinates by using simple form of electric intensity $E$ and pressure anisotropy factor $\Delta$ that involve charge parameter $K$ and anisotropy parameter $\alpha$ respectively. Our solution is well behaved in all respects for all values of $X$ ( $X$ is related to the radius of the star ) lying in the range $0< X \le 0.6$, $\alpha$ lying in the range $0 \le \alpha \le 1.3$, $K$ lying in the range $0< K \le 1.75$ and Schwarzschild compactness parameter "$u$" lying in the range $0< u \le 0.338$. Since our solution is well behaved for a wide range of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We present some models of super dense quark stars and neutron stars corresponding to $X=0.2,~\alpha=0.2$ and $K=0.5$ for which $u_{max}=0.15$. By assuming surface density $\rho_b=4.6888\times 10^{14}~ g/cc$ the mass and radius are $0.955 M_\odot$ and $9.439 km$ respectively. For $\rho_b=2.7\times 10^{14}~ g/cc$ the mass and radius are $1.259 M_\odot$ and $12.439 km$ respectively and for $\rho_b=2\times 10^{14}~ g/cc$ the mass and radius are $1.463 M_\odot$ and $14.453 km$ respectively. It is also shown that inclusion of more electric charge and anisotropy enhances the static stable configuration under radial perturbations. The $M-R$ graph suggests that the maximum mass of the configuration depends on the surface density {\bf i.e. with the increase of surface density} the maximum mass and corresponding radius decrease. This may be because of existence of exotic matters at higher densities that soften the EoSs.

The impact of spheroidicity on the stability of polytropic spheres

We investigate the stability of polytropic spheres in classical general relativity influenced by a departure from homogeneous spherical symmetry. We utilize the Vaidya–Tikekar ansatz to generate models of superdense stars obeying a polytropic equation of state of the form pr=κρ1+1n−β. Models with polytropic index n=1 (quadratic equation of state) and n=2 are generated for the general spheroidal parameter. We investigate the physical viability of these models and show that they describe strange star candidates such as SAX J1808.4-3658 to a good approximation. An interesting finding of this work shows that these models become unstable as the spheroidal parameter is decreased which leads us to conclude that stability is compromised with departure from homogeneous spherical symmetry.

An exact super dense star model on spheroidal space-time

We consider the 3-dimensional space with $t_{1} = \mbox{constant}$ in a super dense star which is spheroidal. We report a class of static spherically symmetric physically viable models based on a particular actual solution of Einsteins field equations. The models of the class admit densities of the order of $2 \times 10^{14}~\mbox{gm}\,\mbox{cm}^{-3}$, radii of the order of a few kilometers and maximum masses up to about three times the solar mass.

Generalized Durgapal–Fuloria relativistic stellar models

We present a new class of closed-form solutions to the Einstein–Maxwell system of equations for a static spherically symmetric anisotropic star in the presence of an electric field by generalizing earlier approaches. The field equations are integrated by specifying the form of the electric field, anisotropic factor, and one of the gravitational potentials which are physically reasonable. We regain some of the earlier solutions of Durgapal and Fuloria (1985), Gupta and Maurya (2011) and Maurya et al. (2015) as special cases. A detailed physical analysis of the solution indicates the physical viability for modelling anisotropic charged superdense stars.

Anisotropic generalization of Vaidya-Tikekar superdense stars

We study superdense relativistic stars with anisotropic matter distributions with spheroidal spatial hypersurfaces. We propose a methodology to make an anisotropic generalization of the Vaidya-Tikekar superdense star model. The anisotropic Einstein field equations can be solved in terms of hypergeometric functions for our choice of gravitational potential and anisotropy. Particular parameter choices allow us to generate models of anisotropic stars in terms of elementary functions. Also, isotropic stars can be generated in the limit of vanishing anisotropy. In particular, we obtain the well known superdense models of Tikekar which are isotropic and have specific spheroidal geometries. The impact of anisotropy on the gross physical behaviour of a compact star is studied.

Relativistic core-envelope anisotropic fluid model of super dense stars

The objective of the present paper is to explore and study an anisotropic spherically symmetric core-envelope model of a super dense star in which core is outfitted with linear equation of state whereas the envelope is considered to be of quadratic equation of state. There is smooth matching between the three regions: the core, envelope and the Schwarzschild exterior metric. We investigate that all the physical and geometrical variables are realistic within the core as well as the envelope of the stellar object and continuous at the junction. Our model is shown to be physically plausible and validate with the intrinsic properties of the neutron star in Vela X-1, SMC X-4 and Her X-1. Further, We infer that with the increase of mass of star the core shrinks, which vindicates the dominating effect of gravity for higher mass astronomical objects.

Core-envelope model of super dense star with distinct equation of states

The aim of the present paper is to study an anisotropic spherically symmetric core-envelope model of a super dense star in which core is equipped with linear equation of state, consistent with the quark matter while the envelope is considered to be of quadratic equation of state by adopting the philosophy of Takisa et al. (Pramana J Phys 92:40, 2019). We demonstrate that all the physical parameters are realistic within the core as well as envelope of the stellar object and continuous at the junction. Our model is shown to be physically viable and substantiate with the strange stars SAX J1808.4-3658 and 4U1608-52. Further, We infer that if the mass of the star increases then central density results to higher values and core shrinks, which justifies the dominating effect of gravity for higher mass celestial objects.

Superdense star in a spacetime with minimal length

In this paper, we generalize core–envelope model of superdense star to a noncommutative spacetime and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein’s field equation in [Formula: see text]-deformed spacetime and use this to set up noncommutative version of core–envelope model describing superdense stars. We derive [Formula: see text]-deformed law of density variation, valid up to first-order approximation in deformation parameter and obtain radial and tangential pressures in [Formula: see text]-deformed spacetime. We also derive [Formula: see text]-deformed strong energy conditions and obtain a bound on the deformation parameter.

Generalized spheroidal spacetimes in 5-D Einstein\u2013Maxwell\u2013Gauss\u2013Bonnet gravity

The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalizes the spheroidal ansatz of Vaidya–Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch–Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss–Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5-dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly.

New interior solution describing relativistic fluid sphere

A new exact solution of embedding class I is presented for a relativistic anisotropic massive fluid sphere. The new exact solution satisfies Karmarkar condition, is well-behaved in all respects, and therefore is suitable for the modelling of superdense stars. Consequently, using this solution, we have studied in detail two compact stars, namely, XTE J1739-289 (strange star $$1.51M_{\odot }$$ , 10.9 km) and PSR J1614-2230 (neutron star $$1.97M_{\odot }$$ , 14 km). The solution also satisfies all energy conditions with the compactness parameter lying within the Buchdahl limit.