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.

Anisotropic Charged Fluid Sphere in Isotropic Coordinates

We have presented a class of charged superdense star models, starting with a static spherically symmetric metric in isotropic coordinates for anisotropic fluid by considering Hajj-Boutros-(1986) type metric potential and a specific choice of electrical intensity E and anisotropy factor Δ which involve charge parameter K and anisotropy parameter α. The solution is well behaved for all the values of Schwarzschild compactness parameter u lying in the range 0<u≤0.2086, for all values of charge parameter K lying in the range 0.04≤K≤0.111 , and for all values of anisotropy parameter α lying in the range 0.016≥α≥0. With the increase in α, the values of K and u decrease. Further, we have constructed a superdense star model with all degree of suitability. The solution so obtained is utilized to construct the models for superdense star like neutron stars ρb=2.7×1014 g/cm3 and strange quark stars ρb=4.6888×1014 g/cm3 . For K=0.06 and α=0.01, the maximum mass of neutron star is observed as M=1.53 M⊙ and radius R=11.48 km. Further for strange quark stars M=1.16 M⊙ and R=8.71 km are obtained.

RELATIVISTIC SOLUTION FOR A CLASS OF STATIC COMPACT CHARGED STAR IN PSEUDO-SPHEROIDAL SPACETIME

Considering Vaidya–Tikekar metric, we obtain a class of solutions of the Einstein–Maxwell equations for a charged static fluid sphere. The physical 3-space (t = const. ) here is described by pseudo-spheroidal geometry. The relativistic solution for the theory is used to obtain models for charged compact objects; thereafter, a qualitative analysis of the physical aspects of compact objects are studied. The dependence of some of the properties of a superdense star on the parameters of the three geometry is explored. We note that the spheroidicity parameter a plays an important role for determining the properties of a compact object. A nonlinear equation of state (EOS) is required to describe a charged compact object with pseudo-spheroidal geometry, which we have shown for known masses of compact objects. We also note that the size of a static compact charged star is more than that of a static compact star without charge.

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 < Ca2 ≤ 0.2645, while its charge analogs are well-behaved for a wide range, 0 < K < 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.