Superdense Stars Research Articles

Stability valley for strange dwarfs

This is a study of the stability of strange dwarfs, superdense stars with a small self-confining core (M core < 0.02 M⊙) containing strange quark matter and an extended crust consisting of atomic nuclei and degenerate electron gas. The mass and radius of these stars are of the same orders as those of ordinary white dwarfs. It is shown that any study of their stability must examine the dependence of the mass on two variables, which can, for convenience, be taken to be the rest mass (total baryon mass) of the quark core and the energy density ρ tr of the crust at the surface of the quark core. The range of variation of these quantities over which strange dwarfs are stable is determined. This region is referred to as the stability valley for strange dwarfs. The mass and radius from theoretical models of strange dworfs are compared with observational data obtained through the HIPPARCOS program and the most probable candidate strange dwarfs are identified.

Analytic Well Behaved Charged Relativistic Super-dense Star Models

In the present article, we have obtained a new class of well behaved charged super-dense star models after prescribing a particular form of the metric potential and electric intensity. The metric describing the super-dense stars model joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. The interior of the stars possess there energy density, pressure, pressure-density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface

Generalised Buchdahal Solution via Solution Generating Scheme

Two particular cases of perfect fluid solution for the parameter K=-2, Buchdahal [1] are generalised to yield two new perfect fluid solutions using a solution generating theorem, Petarpa et. al. [2]. The fluid spheres so obtained are utilised to construct two super-dense stars models with surface density 2×1014gmcm-3. The maximum mass and the corresponding radii for the newly obtained models are given as 5.7693 MΘ, 17.8074km and 0.2330 MΘ, 5.9290km.

Variety of well behaved exact solutions of Einstein–Maxwell field equations: an application to Strange Quark stars, Neutron stars and Pulsars

We present a variety of well behaved classes of Charge Analogues of Tolman’s iv (1939). These solutions describe charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. These solutions give us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. keeping in view of well behaved nature of these solutions, one new class of solutions is being studied extensively. Moreover, this class of solutions gives us wide range of constant K (0.3≤K≤0.91) for which the solution is well behaved hence, suitable for modeling of super dense stars like Strange Quark stars, Neutron stars and Pulsars. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Quark stars, Neutron stars and Pulsars. By assuming the surface density ρ b =2×1014 g/cm3 (like, Brecher and Caporaso in Nature 259:377, 1976), corresponding to K=0.30 with X=0.39, the resulting well behaved model has the mass M=2.12M Θ, radius r b ≈15.27 km and moment of inertia I=4.482×1045 g cm2; for K=0.4 with X=0.31, the resulting well behaved model has the mass M=1.80M Θ, radius r b ≈14.65 km and moment of inertia I=3.454×1045 g cm2; and corresponding to K=0.91 with X=0.135, the resulting well behaved model has the mass M=0.83M Θ, radius r b ≈11.84 km and moment of inertia I=0.991×1045 g cm2. For n=0 we rediscovered Pant et al. (in Astrophys. Space Sci. 333:161, 2011b) well behaved solution. These values of masses and moment of inertia are found to be consistent with other models of Neutron stars and Pulsars available in the literature and are applicable for the Crab and the Vela Pulsars.

A Class of Charged Relativistic Superdense Star Models

In this article we obtain a new class of well behaved charged solutions by using particular forms of the metric potential g44 and electric intensity, which involves a parameter K. The metric describing the superdense stars joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. This class of solutions describes well behaved charged fluid balls. The class of solutions gives range of parameter K (0.13≤K≤1.9999) for which the solution is well behaved hence, suitable for modeling of super dense star. The interior of the stars possess there energy density, pressure, pressure-density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface. In view of the surface density 2×1014 gm/cm3, the maximum mass of the charged fluid balls and corresponding radius are 0.4711MΘ and 7.0122 km. The red shift at the centre and boundary are found to be 0.1640 and 0.1100 respectively.

Exact solutions: neutral and charged static perfect fluids with pressure

We show in this article that charged fluid with pressure derived by Bijalwan (Astrophys. Space. Sci. doi:10.1007/s10509-011-0691-0, 2011a) can be used to model classical electron, quark, neutron stars and pulsar with charge matter, quasi black hole, white dwarf, super-dense star etc. Recent analysis by Bijalwan (Astrophys. Space. Sci., 2011d) that all charged fluid solutions in terms of pressure mimic the classical electron model are partially correct because solutions by Bijalwan (Astrophys. Space. Sci. doi:10.1007/s10509-011-0691-0, 2011a) may possess a neutral counterpart. In this paper we characterized solutions in terms of pressure for charged fluids that have and do not have a well behaved neutral counter part considering same spatial component of metric eλ for neutral and charged fluids. We discussed solution by Gupta and Maurya (Astrophys. Space Sci. 331(1):135–144, 2010a) and solutions by Bijalwan (Astrophys. Space Sci. doi:10.1007/s10509-011-0735-5, 2011b; Astrophys. Space Sci. doi:10.1007/s10509-011-0780-0, 2011c; Astrophys. Space Sci., 2011d) such that charged fluids possess and do not possess a neutral counterpart as special cases, respectively. For brevity, we only present some analytical results in this paper.

A new family of polynomial solutions for charged fluid spheres

We present a new family of relativistic charged fluid spheres described by a space time metric with a prescribed metric potential g 44 along with the specific choice of electric field intensity which vanishes at the centre and monotonically increasing towards the pressure free surface. The charged fluid solutions so obtained satisfy all the energy conditions along with the velocity of sound which decreases away from the centre. Also the solutions are utilized to construct the models of super-dense stars.

New class of well behaved exact Solutions for static charged Neutron-star with perfect fluid

The paper presents a class of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged fluid. This class of solutions describes well behaved charged fluid balls. This solution gives us wide range of parameter K (0.53≤K≤0.95), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to K=0.95 with X=−0.15, the maximum mass of the star comes out to be M=1.56 MΘ with radius rb≈9.22 km and the surface red shift Zb≈0.124207. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of neutron star. However, its neutral counter part is not well behaved.

Closed form charged fluid with t = constant hypersurfaces as spheroids and hyperboloids

In the present article models of well behaved charged superdense stars with surface density 2×1014 gm/cm3 are constructed by considering a static spherically symmetric metric with t = const hypersurfaces as spheroids and hyperboloids. Maximum mass of the star is found to be 7.66300MΘ with radius 19.35409 km for spheroids case while 1.51360MΘ with radius 13.72109 km for hyperboloid case satisfying ultra-relativistic conditions. The solutions thus found satisfy all the reality and causality conditions. For brevity we don’t present a detailed analysis of the derived solutions in this paper.

REGULAR AND WELL-BEHAVED RELATIVISTIC CHARGED SUPERDENSE STAR MODELS

A new class of charged superdense star models is obtained by using an electric intensity, which involves two parameters, K and n. The metric describing the model shares its metric potential g44 with that of Durgapal's fourth solution.1 The pressure-free surface is kept at the density 2 × 1014 g/cm 3and joins smoothly the Reissner–Nordstrom solution. The neutral solution is well-behaved for 0 &lt; Ca2 ≤ 0.2645, while its charge analogs are well-behaved for a wide range, 0 &lt; K &lt; 32, i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.1826 MΘ and 19.7120 km, respectively for Ca2 = 0.2645, while the redshift at the center and at the surface are given by Z0 = 1.6444 and Za = 0.6538, respectively. For the charged solution, the maximum mass and radius are 6.3811MΘ and 19.1609 km, respectively for K = 1.4, n = 1 and Ca2 = 0.5016, with the redshift at the center Z0 = 3.7437 and at the surface Za = 1.1038.

A class of well behaved charged superdense star models of embedding class one

A class of well behaved charged superdense star models of embedding class one is obtained by taking perfect fluid to be interior matter. In the process we come across the models for white dwarf, quark and neutron stars. Maximum mass of the star of this class is found to be 6.716998MΘ with its radius is 18.92112 Km. In the absence of charge the models reduce to Schwarzchild’s interior model with constant density.

Extremization of mass of charged superdense star models describe by Durgapal type space-time metric

In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g44=B(1+Cr2)n, where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved.

Closed form Vaidya-Tikekar type charged fluid spheres with pressure

Recently, Bijalwan (Astrophys. Space Sci. doi:10.1007/s10509-011-0691-0, 2011) discussed all important solutions of charged fluid spheres with pressure and Gupta et al. (Astrophys. Space Sci. doi:10.1007/s10509-010-0561-1, 2010) found first closed form solutions of charged Vaidya-Tikekar (V-T) type super-dense star. We extend here the approach evolved by Bijalwan (Astrophys. Space Sci. doi:10.1007/s10509-011-0691-0, 2011) to find all possible closed form solutions of V-T type super-dense stars. The existing solutions of Vaidya-Tikekar type charged fluid spheres considering particular form of electric field intensity are being used to model massive stars. Infact at present maximum masses of the star models are found to be 8.223931MΘ and 8.460857MΘ subject to ultra-relativistic and non-relativistic conditions respectively. But these stars with such are large masses are not well behaved due to decreasing velocity of sound in the interior of star. We present new results concerning the existence of static, electrically charged perfect fluid spheres that have a regular interior. It is observed that electric intensity used in this article can be used to model superdense stars with ultrahigh surface density of the order 2×1014 gm/cm3 which may have maximum mass 7.26368240MΘ for ultra-relativistic condition and velocity of sound found to be decreasing towards pressure free interface. We solve the Einstein-Maxwell equations considering a general barotropic equation of state with pressure. For brevity we don’t present a detailed analysis of the derived solutions in this paper.

New class of Well behaved exact solutions of relativistic charged white-dwarf star with perfect fluid

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92MΘ with radius rb≈17.15 km and the surface red shift Zb≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.

A class of well behaved charged analogues of Vaidya–Tikekar type super-dense star

In the present article a model of well behaved charged superdense star with surface density 2×1014 gm/cm3 is constructed by considering a static spherically symmetric metric with t=const hypersurfaces as hyperboloid. So far well behaved model described by such metric could not be obtained. Maximum mass of the star is found to be 0.343457M⊙ and the corresponding radius is 9.57459 km. The red shift at the centre and on the surface are given as 0.068887 and 0.031726 respectively.

On a family of well behaved perfect fluid balls as astrophysical objects in general relativity

A family of well behaved perfect fluid balls has been derived starting with the metric potential g44=B(1+Cr2)n for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c2ρ≥p≥0,dp/dr 1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×1014 gm/cm3. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848MΘ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z0=1.6459 and Za=0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 MΘ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I1) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3 corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5MΘ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.

Well Behaved Class of Charge Analogue of Durgapal’s Relativistic Exact Solution

We obtain a new class of charged super-dense star models after prescribing particular Forms of the metric potential and electric intensity. The metric describing the superdense stars joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. The interior of the stars possess their energy density, pressure, pressure density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface. In view of the surface density ρb=2×1014g/cm3, the heaviest star occupies a mass 5.523 M⊙with its radius 13.98 km. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal [1].

Well Behaved Class of Charge Analogue of Adler’s Relativistic Exact Solution

We present a well behaved class of charge analogue of Alder’s (1974). This solution describes charge fluid balls with positively finite central pressure and positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.96 ≤ K ≤ 5.2) for which the solution is well behaved and appropriate for relativistic theory; therefore, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degrees of suitability and by assuming the surface density ρb = 2 × 1014 g/cm3. Corresponding to K = 0.96 and X = 0.35, the maximum mass of the star comes out to be 3.43 MΘ with linear dimension 32.66 Km and central redshift and surface redshift 1.09374 and 0.5509 respectively.

Well Behaved Parametric Class of Exact Solutions of Einstein-Maxwell Field Equations in General Relativity

We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb = 2 × 1014g/cm3. Corresponding to K = 0.72 with X = 0.15, the resulting well behaved model has the mass M = 1.94 MΘ with radius rb » 15.2 km and for K = 2.41 with X = 0.15, the resulting well behaved model has the mass M = 2.26 MΘ with radius rb » 14.65 km.