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.     

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

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 form of charge distribution. This class of solutions gives us wide range of parameters, n and K, for which the solutions are well behaved hence, suitable for modeling of compact star (e. g. bare strange quark star). The mass of star is maximized with all degree of suitability 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 help in connection of some study of stellar structure.     

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.     

Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . Maxwell’s equation

Higher dimensional exact solutions for a charged fluid sphere in general theory of relativity

The exact higher dimensional solutions of Einstein-Maxwell field equations for spherically symmetric distribution of charged perfect fluid are obtained by using the method originally used by Hajj-Boutros and Sfeila (Gen. Relativ. Gravit. 18(4):395, 1986) for four-dimensional space-time. The new exact solutions have been generated from those of Khadekar et al. (J. Indian Math. Soc. 68(1–4):33, 2001), Humi and Mansour (Phys. Rev. D 29(6):1076, 1984) and Banerjee and Santos (J. Math. Phys. 22(4):824, 1981) in the frame work of higher dimensional space-time. The various physical properties are also discussed.     

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).     

Study of a new class of cylindrically symmetric space-time in general relativity

A new class of solutions of Einstein field equations is investigated for a cylindrically symmetric space-time when the source of gravitation is a perfect fluid. To get the deterministic solution a relation between metric coefficients A=(BC) ⁿ is assumed. Certain physical and geometric properties of the model are also discussed.     

Exact Kantowski–Sachs cosmological models in general theory of relativity

We have studied cosmological model generated by perfect fluid coupled with mass less scalar field for Kantowski–Sachs space–time in general theory of relativity. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. Some physical consequences of the models have been discussed in case of Zel’dovich fluid.     

Role of a tachyonic field in accelerating the Universe in the presence of a perfect fluid

Recently, a tachyonic field was presented as a dark energy model to represent the present acceleration of the Universe. In this paper, we consider a mixture of tachyonic fluid with a perfect fluid. For this purpose we consider barotropic fluid and Generalized Chaplygin gas (GCG). We present a particular form of the scale factor. We solve the equations of motion to get exact solutions of the density, tachyonic potential and the tachyonic field. We introduce a coupling term to show that the interaction decays with time. We also show that the nature of the potentials vary, so the interaction term reduces the potential in both cases.     

Accretion disks in bimetric theory of gravitation. A strong field test of general relativity?

The sensitivity of accretion disk models with respect to its inner boundary conditions, being located in the strong gravity region of a highly compact central body, is used to discuss a possibility of strong field tests of gravitation via compact source observations. Within the bimetric theory of gravitation the optically thin bremsstrahlung model is calculated as an example for this possibility. Using this model to describe the innermost region of the “bimetric disk”, significant differences with respect to the corresponding results in Einstein's theory were found. The more massiv and compact “bimetric disk” radiates softer with higher luminosity.     

Charged analogue of Vlasenko-Pronin superdense star in general relativity

In this article we have derived a set of three static spherical symmetric well behaved solutions of Einstein-Maxwell field equations is obtained for a specific choice of electric field involving a parameter K. The solutions so obtained can be seen as a charge analogue of the neutral solution due to Vlasenko and Pronin. The physical features of solutions so obtained and that of Vlasenko and Pronin are investigated subject to the reality and the causality conditions i.e. Pressure, density (greater than pressure), pressure-density ratio and velocity of sound (less than the velocity of light) are positive and monotonically decreasing and the electric intensity is monotonically increasing in nature away from the centre. The maximum mass and radius occupied by the neutral solution are 2.1434 M _Θ and 16.7300 km respectively. For the charged solution, overall maximum mass and corresponding radius are found to be 6.8714 M _Θ and 20.6166 km respectively (for K=1.343).     

Exact Bianchi type-V perfect fluid cosmological models in Brans–Dicke theory of gravitation

Exact Bianchi type-V cosmological models are obtained in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961) in the presence of perfect fluid distribution. Some physical and geometrical properties of the models are also discussed.     

A class of exact isotropic solutions of Einstein’s equations and relativistic stellar models in general relativity

In this paper we have studied a particular class of exact solutions of Einstein’s gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/c ² R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538–52, LMC X-4, SAX J1808.4?3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.     

Plane symmetric inhomogeneous cosmological models with a perfect fluid in General Relativity II

We investigate a class of solutions of Einstein equations for the plane symmetric perfect fluid case. If these solutions have shear, they must necessarily be non-static. Some physical and geometric properties of the models are also discussed.      

Infrared photometry for variable stars of selected types in 1978–1999

We present and discuss IR observations for 35 stars of different variability types averaged over many years. These include about twenty symbiotic stars, four W Ser stars and one Algol, six Miras, etc.     

Final evolution of stars in the range 103–104 M ⊙

The final dynamical collapse of oxygen cores of 10³ and 10⁴ M which undergo the pair formation instability is computed. These cores are found to suffer complete collapse, presumably to form black holes, in contrast to cores of 100M which have previously been found to explode completely, leaving no remnant. These calculations represent a first attempt to ascertain the outcome of evolution over several decades of mass previously unexplored. The outcome may have some relevance to models of X-ray sources in globular clusters.     

Incompatibility of five dimensional LRS Bianchi type-V string and mesonic string cosmological models in general relativity

In this paper, we constructed some cosmological models in five dimensional LRS Bianchi type-V space time based on general theory of relativity. Further, it is shown that source density of the meson field does not survive either in massive scalar field or in mass less scalar field. Some physical and geometrical properties of the models are discussed.     

Neutron star mergers in the context of the hadron–quark phase transition

The long awaited event of the detection of a gravitational wave from a binary neutron star merger and its electromagnetic counterparts marked the beginning of a new era in observational astrophysics. The brand-new field of gravitational wave astronomy combined with multi-messenger observations will uncover violent, highly energetic astrophysical events that could not be explored before by humankind. This article focuses on the presumable appearance of a hadron–quark phase transition and the formation of regions of deconfined quark matter in the interior of a neutron star merger product. The evolution of density and temperature profiles inside the inner region of the produced hypermassive/supramassive neutron star advises an incorporation of a hadron–quark phase transition in the equation of state of neutron star matter. The highly densed and hot neutron star matter of the remnant populate regions in the QCD phase diagram where a non neglectable amount of deconfined quark matter is expected to be present. If a strong hadron–quark phase transition would happen during the post-merger phase, it will be imprinted in the spectral properties of the emitted gravitational wave signal and might give an additional contribution to the dynamically emitted outflow of mass.