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Permanent URI for this collectionhttps://hdl.handle.net/10361/6793

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A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars
(© 2017, Springer New York LLC, 2/1/2017) Singh, Ksh Newton; Murad, Mohammad Hassan; Pant, Neeraj; Department of Mathematics and Natural Sciences
The present paper provides a new model of compact stars satisfying the Karmarkar condition. The model is obtained by assuming a new type of metric potential for gr r from the condition of embedding class I. The model parameters are obtained accordingly by employing the metric potentials to Einstein's field equations. Our model is free from geometric singularity and satisfies all the physical conditions. The obtained mass and radius of the compact stars Cen X-3, EXO 1785-248 and SAX 1808.4-3658 obtained from the model are consistent with the observational data of T. Gangopadhyay et al. Detailed analyses of these neutron stars (Cen X-3, EXO 1785-248 and SAX 1808.4-3658) are also given with the help of graphical representations.
A class of relativistic anisotropic charged stellar models in isotropic coordinates
(© 2014, Springer Science+Business Media Dordrecht., 2014) Pant, Neeraj; Pradhan, Nirakar; Murad, Mohammad Hassan; Department of Mathematics and Natural Sciences
In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters: 4<n≤21.6, 0<K<0.2499, 0≤α≤0.068 and Schwarzschild parameter, 0≤u=GM/c2R≤0.334. With Δ=0 we rediscover the isotropic model of Pant et al. (Astrophys. Space Sci. 352:135, 2014) and with α=0 and K=0 we rediscover the isotropic neutral model of Murad and Pant (Astrophys. Space Sci. 350:349, 2014). It has been observed that with the increase of α maximum mass decreases. We also present models of super dense star like neutron and quark star based on the particular solution taking n=4.35, α=0.002, K=0.2062 for which u has maximum value umax=0.306. By assuming surface density ρb=4.6888×1014 g cm−3 the resulting well behaved solution has a maximum quark star mass M=2.02 M⊙ and radius R=9.78 km; and the choice ρb=2.7×1014 g cm−3 results charged fluid ball of maximum mass M=2.66 M⊙ and radius R=12.89 km.
A class of super dense stars models using charged analogues of Hajj-Boutros type relativistic fluid solutions
(© 2014, Springer Science+Business Media New York, 2014-10) Pant, Neeraj; Pradhan, Nirakar; Murad, Mohammad Hassan; Department of Mathematics and Natural Sciences
We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for perfect charged fluid, compatible with a super dense star modeling. The solution is well behaved for all the values of Schwarzschild parameter u lying in the range 0 < u < 0.1727 for the maximum value of charge parameter K = 0.08163. The maximum mass of the fluid distribution is calculated by using stellar surface density as ρb = 4.6888×1014g cm−3. Corresponding to K = 0.08 and umax = 0.1732, the resulting well behaved solution has a maximum mass M = 0.9324M⊙ and radius R = 8.00 and by assuming ρb = 2×1014g cm−3 the solution results a stellar configuration with maximum mass M = 1.43M⊙ and radius Rb = 12.25 km. The maximum mass is found increasing with increasing K up to 0.08. The well behaved class of relativistic stellar models obtained in this work might has astrophysical significance in the study of internal structure of compact star such as neutron star or self-bound strange quark star like Her X-1.
Anisotropic charged stellar models in Generalized Tolman IV spacetime
(© 2015, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015) Murad, Mohammad Hassan; Fatema, Saba; Department of Mathematics and Natural Sciences
With the presence of electric charge and pressure anisotropy some anisotropic stellar models have been developed. An algorithm recently presented by Herrera et al. (Phys. Rev. D 77, 027502 (2008)) to generate static spherically symmetric anisotropic solutions of Einstein's equations has been used to derive relativistic anisotropic charged fluid spheres. In the absence of pressure anisotropy the fluid spheres reduce to some well-known Generalized Tolman IV exact metrics. The astrophysical significance of the resulting equations of state (EOS) for a particular case (Wyman-Leibovitz-Adler) for the anisotropic charged matter distribution has been discussed. Physical analysis shows that the relativistic stellar structure obtained in this work may reasonably model an electrically charged compact star, whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself like electrically charged bare strange quark stars.
Relativistic anisotropic stellar models with Tolman VII spacetime
(© 2015, Springer Science+Business Media Dordrecht, 2015-09) Bhar, Piyali; Murad, Mohammad Hassan; Pant, Neeraj; Department of Mathematics and Natural Sciences
In this paper we have studied the behavior of static spherically symmetric relativistic objects with locally anisotropic matter distribution considering the Tolman VII form for the gravitational potential grr in curvature coordinates together with the linear relation between the energy density and the radial pressure. The interior spacetime has been matched continuously to the exterior Schwarzschild geometry. We have investigated and analyzed different physical properties of the stellar model and presented graphically.
Relativistic compact anisotropic charged stellar models with Chaplygin equation of state
(© Springer Science+Business Media Dordrecht 2016, 2016) Bhar, Piyali; Murad, Mohammad Hassan; Department of Mathematics and Natural Sciences
This paper presents a new model of static spherically symmetric relativistic charged stellar objects with locally anisotropic matter distribution together with the Chaplygin equation of state. The interior spacetime has been matched continuously to the exterior Reissner–Nordström geometry. Different physical properties of the stellar model have been investigated, analyzed, and presented graphically.
Some analytical models of anisotropic strange stars
(© Springer Science+Business Media Dordrecht 2015, 2016) Murad, Mohammad Hassan; Department of Mathematics and Natural Sciences
Over the years of the concept of local isotropy has become a too stringent condition in modeling relativistic self-gravitating objects. Taking local anisotropy into consideration, in this work, some analytical models of relativistic anisotropic charged strange stars have been developed. The Einstein–Maxwell gravitational field equations have been solved with a particular form of one of the metric potentials. The radial pressure and the energy density have been assumed to follow the usual linear equation of state of strange quark matter, the MIT bag model.
Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling
(© The Author(s) 2015. This article is published with open access at Springerlink.com, 2015) Murad, Mohammad Hassan; Fatema, Saba; Department of Mathematics and Natural Sciences
In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein–Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

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