A well-behaved class of charged analogue of Durgapal solution

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes 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. This solution gives 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 this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤K≤2.2) 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 solution 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 Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03M _Θ , radius r _b =19.53 km and moment of inertia I=1.213×10⁴⁶ g?cm²; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43M _Θ , radius r _b =18.04 km and moment of inertia I=1.136×10⁴⁶ g?cm²; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56M _Θ , radius r _b =17.30 km and moment of inertia I=1.076×10⁴⁶ g?cm². These values of masses and moment of inertia are found to be consistent with the crab pulsars.     

A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. The maximum mass of the Neutron star comes out to be M=1.591 M _Θ with radius R _b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.     

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 ρ _b =2×10¹⁴ g/cm³ corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M _Θ 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.     

Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These 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 centre. 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, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

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.     

Well behaved class of charge analogue of Heintzmann’s relativistic exact solution

We present a well behaved class of Charge Analogue of Heintzmann (Z. Phys. 228:489, 1969) solution. 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 constant K (1.25≤K≤15) for which the solution is well behaved and 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 ρ _b =2×10¹⁴ g/cm³. Corresponding to K=1.25 and X=0.42, the maximum mass of the star comes out to be 3.64M _Θ with linear dimension 24.31 km and central redshift 1.5316.     

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity

This paper presents a new family of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ _nm=2.5×10¹⁷ kg?m^?3. By this model we obtain the mass of the Crab pulsar, M _Crab, 1.36M _⊙ and radius 13.21 km, constraining the moment of inertia >?1.61×10³⁸ kg?m² for the conservative estimate of Crab nebula mass 2M _⊙. And M _Crab=1.96M _⊙ with radius R _Crab=14.38 km constraining the moment of inertia >?3.04×10³⁸ kg?m² for the newest estimate of Crab nebula mass, 4.6M _⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I _A =1.4285×10³⁸ kg?m² and I _B =1.3647×10³⁸ kg?m² respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M _G(max)=4.7487M _⊙ with radius $R_{M_{\max}}=15.24~\mathrm{km}$ , surface redshift 0.9878, charge 7.47×10²⁰ C, and central density 4.31ρ _nm.     

New parametric classes of exact solutions in general relativity and polytropic nature fluid ball with constant sound speed

In this paper we have presented a method of obtaining varieties of new parametric classes of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions has been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less then one. From the solutions of one of the class we have constructed a causal model of polytrope with constant sound speed Corresponding to the polytrope model we have maximized the Neutron star mass 3.26 M_⊙ with the linear dimensions 32.27 kms with surface red shift 0.7355 and for other class we have constructed a causal model in which outmarch of pressure and density is monotonically decreasing and pressure–density ratio is positive and less than 1 throughout with in the ball. Corresponding to this model we have maximized the Neutron star mass 3.09 M_⊙ with the linear dimensions 30.55 kms with surface red shifts 0.5811.     

A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K (0.69≤K≤7.1), for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density ρ _nm=2.5×10¹⁷kg?m^?3. By this model we obtain the mass of the Crab pulsar M _Crab=1.401M _⊙ and the radius, R _Crab=12.98 km constraining the moment of inertia I _NS,38>1.61 for the conservative estimate of Crab nebula mass 2M _⊙ and M _Crab=2.0156M _⊙ with radius, R _Crab=14.07 km constraining the moment of inertia I _NS,38>3.04 for the newest estimate of Crab nebula mass 4.6M _⊙ which are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are I _A,38=1.4624 and I _B,38=1.2689 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020M _⊙ with radius 14.49 km, surface redshift z _R =0.4319, charge Q=4.67×10²⁰ C, and central density ρ _c =2.68ρ _nm.     

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 g ₄₄=B(1+Cr ²) 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. c ² ρ≥p≥0,dp/dr<0,dρ/dr<0, along with the velocity of sound \((\sqrt{dp/c^{2}d\rho} )< 1\) and the adiabatic index ((p+c ² ρ)/p)(dp/(c ² dρ))>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 4.1848M _Θ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z ₀=1.6459 and Z _a =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 M _Θ 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.     

New class of Well behaved exact solutions of relativistic charged <Emphasis Type="Italic">white-dwarf</Emphasis> 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 ρ _b =2×10¹⁴ g/cm³. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92M _Θ with radius r _b ≈17.15 km and the surface red shift Z _b ≈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 generalized charged analogues of Vaidya-Tikekar type fluid sphere in general relativity

In this paper first ever we have developed a class of well behaved charged fluid spheres expressed by a space time with its hypersurfaces $t = \operatorname {const}$ . as spheroid for the case 0<K<1 with surface density 2×10¹⁴ gm/cm³. The same utilized to construct a superdense star and seen that star satisfies all well behaved condition for 0<K≤0.038. The maximum mass occupied and the corresponding radius are found to be 4.830982M _Θ and 20.7612 km respectively. The redshift at the center and on the surface is given z ₀=0.425367 and z _a =0.240901.     

A family of well behaved charge analogues of?a?well behaved neutral solution in?general relativity

A family of charge analogues of a neutral solution with g ₄₄=(1+Cr ²)⁶ has been obtained by using a specific electric intensity, which involves a parameter K. Both neutral and charged solutions are analysed physically subject to the surface density 2×10¹⁴ gm/cm³ (neutron star). The neutral solution is well behaved for 0.0<Ca ²≤0.10477 while its charge analogues are well behaved for a wide range of a parameter K (0≤K≤72) i.e. pressure, density, pressure-density ratio, velocity of sound is monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and radius occupied by the neutral solution are 3.4126M _Θ and 18.9227 km for Ca ²=0.10447 respectively. While the red shift at centre Z ₀=0.9686 and red shift at the surface Z _a =0.4612. For the charged solution, the maximum mass and radius are 5.6111M _Θ and 17.2992 km respectively for K=3.0130 and Ca ²=0.2500, with the red shift Z ₀=3.0113 and Z _a =1.0538.     

A class of charged analogues of Durgapal and Fuloria superdense star

We obtain a new class of charged super-dense star models after prescribing particular forms of the metric potential g ₄₄ 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 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 g/cm³, the heaviest star occupies a mass 5.6996 M _⊙ with its radius 17.0960 km. The red shift at the centre and boundary are found to be 3.5120 and 1.1268 respectively. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982).     

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: I. Cosmic microwave background radiation

Using the explicit form of the functions to describe the monopole and dipole spectra of the Cosmic Microwave Background (CMB) radiation, the exact expressions for the temperature dependences of the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume, and pressure in the finite range of frequencies v ₁≤v≤v ₂ are obtained. Since the dependence of temperature upon the redshift z is known, the obtained expressions can be simply presented in z representation. Utilizing experimental data for the monopole and dipole spectra measured by the COBE FIRAS instrument in the 60–600 GHz frequency interval at the temperature T=2.72548 K, the values of the radiative and thermodynamic functions, as well as the radiation density constant a and the Stefan-Boltzmann constant σ are calculated. In the case of the dipole spectrum, the constants a and σ, and the radiative and thermodynamic properties of the CMB radiation are obtained using the mean amplitude T _amp=3.358 mK. It is shown that the Doppler shift leads to a renormalization of the radiation density constant a, the Stefan-Boltzmann constant σ, and the corresponding constants for the thermodynamic functions. The expressions for new astrophysical parameters, such as the entropy density/Boltzmann constant, and number density of CMB photons are obtained. The radiative and thermodynamic properties of the Cosmic Microwave Background radiation for the monopole and dipole spectra at redshift z≈1089 are calculated.     

Well behaved parametric class of relativistic charged fluid ball in?general relativity

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≤K≤42) 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 ρ _b =2×10¹⁴ g/cm³. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M _Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).     

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.     

A family of exact solutions of Einstein-Maxwell field equations in isotropic coordinates: an application to optimization of quark star mass

In the present paper, we have obtained a class of charged super dense star models, starting with a static spherically symmetric metric in isotropic coordinates for perfect fluid by considering Hajj-Boutros (in J. Math. Phys. 27:1363, 1986) type metric potential and a specific choice of electrical intensity which involves a parameter K. The resulting solutions represent charged fluid spheres joining smoothly with the Reissner-Nordstrom metric at the pressure free interface. The solutions so obtained are utilized to construct the models for super-dense star like neutron stars (ρ _b =2 and 2.7×10¹⁴ g/cm³) and Quark stars (ρ _b =4.6888×10¹⁴ g/cm³). Our solution is well behaved for all values of n satisfying the inequalities \(4 < n \le4(4 + \sqrt{2} )\) and K satisfying the inequalities 0≤K≤0.24988, depending upon the value of n. Corresponding to n=4.001 and K=0.24988, we observe that the maximum mass of quark star M=2.335M _⊙ and radius R=10.04 km. Further, this maximum mass limit of quark star is in the order of maximum mass of stable Strange Quark Star established by Dong et al. (in arXiv:1207.0429v3, 2013). The robustness of our results is that the models are alike with the recent discoveries.     

A class of new solutions of generalized charged analogues of Buchdahl’s type super-dense star

The present paper reports a class of new solutions of charged fluid spheres expressed by a space time with its hypersurfaces t=const. as spheroid for the case 0<K<1 with surface density 2×10¹⁴ gm/cm³. When the Buchdahl’s type fluid spheres are electrified with generalized charged intensity and it is utilized to construct a super-dense star and found that star satisfies all reality conditions except the casual condition for 0<K≤0.05. The maximum mass occupied and the corresponding radius have been obtained 8.130871 M _Θ and 24.60916 km respectively. Further, the redshift at the centre and on the surface are noted by z ₀=0.933729 and z _a =0.383808 respectively.     

Charged fluid to anisotropic fluid distribution in general relativity

A new class of well behaved anisotropic super-dense stars has been derived with the help of a given class of charged fluid distributions. The anisotropy parameter (or the electric intensity) is zero at the centre and monotonically increasing towards the pressure free interface. All the physical parameter such as energy density, radial pressure, tangential pressure and velocity of sound are monotonically decreasing towards the surface. The maximum mass measures 3.8593 solar mass and the corresponding radius is 21.2573 km for n=1 i.e. N tends to infinity.