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

Abstract

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 ( dp/c 2 dρ) < 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 × 10 14 gm/cm 3 . 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 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 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.

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

“…Ishak et al [175], Lake [176], and recently Maurya and Gupta [107,157] showed that the ansatz for the metric function (2.1.14) produces an infinite family of analytic solutions of the self-bound type. Five of these were previously known (N = 1, 2, 3, 4, and 5).…”

“…The principal motivation of this work is to develop some new analytical relativistic stellar models by obtaining closedform solutions of Einstein-Maxwell field equations following the approach of Durgapal [13], and of Maurya and Gupta [107,157]. Our analysis depends on several mathematical key assumptions.…”

New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model

“…For ordinary strange matter, the electric field is ~ 10 18 V/cm to up to 10 19 V/cm if SQS forms a color superconductor [9][10]. The electric fields are as high as 10 [19][20] V/cm [13] and it's determined the electrostatic effects and the surface tension of the interface between vacuum and quark matter [14]. And interesting things is that our model is exactly matching that range [13] of electric field.…”

“…Thus these choices are physically reasonable and useful in the study of the gravitational behavior of charged stellar objects. It has been shown by Maurya and Gupta [19,20] for the uncharged and charged cases respectively that the ansatz for the metric function…”

Anisotropic charged physical models with generalized polytropic equation of state

“…Pant et al [6] shown that a charged solution possess positively finite pressure and density at the center which fulfill the casuality condition, i.e., d P r dρ ≤ 1. Maurya and Gupta [7,8] derived a e-mail: ayishanasim2@gmail.com b e-mail: azam.math@ue.edu.pk charged solutions with metric potential g 44 = B(1 + Cr 2 ) n for every integral value of n, by specifying electric field intensity in terms of parameter K and remarked that all solutions for n ≥ 4 are well behaved for some range of parameter K.…”