International Journal of Astrophysics and Space Science 2014; 2(3): 46-55 Published online August 20, 2014 (http://www.sciencepublishinggroup.com/j/ijass) doi: 10.11648/j.ijass.20140203.12 Well behaved charge analogues of Wyman-Adler exact solution for a self-bound star A. H. M. Mahbubur Rahman 1, * , M. Rubayet Rahman 2 , A. S. M. Mohiul Islam 3 1 Department of Civil Engineering, Southern University Bangladesh, Bangladesh 2 Faculty of Math and Science, Asian University for Women, Bangladesh 3 Department of Mathematics, University of Chittagong, Bangladesh Email address: rahman.m.cu@gmail.com (A. H. M. M. Rahman), rubayet.rahman01@gmail.com (M. R. Rahman), lc_pinto_mathcu@yahoo.com (A. S. M. M. Islam) To cite this article: A. H. M. Mahbubur Rahman, M. Rubayet Rahman, A. S. M. Mohiul Islam. Well Behaved Charge Analogues of Wyman-Adler Exact Solution for a Self-Bound Star. International Journal of Astrophysics and Space Science. Vol. 2, No. 3, 2014, pp. 46-55. doi: 10.11648/j.ijass.20140203.12 Abstract: The exact analytical Wyman-Adler’s relativistic solution describing the interior of a charged spherical strange star candidate is found under the assumption and existence of two parameters K and m. The interior self-bound star matter, pressure, energy density and the adiabatic sound speed are represented in terms of simple algebraic function. The analytic solution depicts a unique static charged configuration of quark matter with radius R~9 km and total mass M~2.5M⊙. And try to investigate the velocity of sound approximately 1/√3 which is similar to the attitude of SQM (Strange Quark matter). Based on analytic model in the recent work, the applicable values of physical quantities have been calculated by accepting the estimated masses and radii of some well-known strange star candidates like PSR J1903+327, Her X-1, Cen X-3, EXO 1785-248. The equation of state of the charge matter distribution may play a major role in the study of the interior structure of highly compact charge stellar object in astrophysical study. Keywords: Exact Solution, Einstein-Maxwell, Reissner–Nordström, Relativistic Astrophysics, Compact Star, Equation of State 1. Introduction It is well known that, at the pressure free interface, the Reissner-Nordstrӧm solution is interesting to observe (present charge) the gravitational collapse of a spherical symmetric distribution of the matter to a point singularity may be avoided [1] if the matter distribution acquires large amount of electric charge. Any compact star is not composed of charged perfect fluid and may be used to make a suitable model of compact object with charge matter for the numerical study of the stellar structure [2, 3, 4]. Pant, Metha and Tewari showed that radiative gravitational radiation (GR) collapse may be contributed to formation of the compact non-singular massive hot object [5-7]. The black hole is never formed due to the apparent horizon formation condition [8]. This could be understood as the formation of a naked singularity. But the main reason is that the star radiates all its mass before it reaches the singularity at r = 0 and t = 0. Nuclear matter is meta-stable and it is well known that after releasing a lot of energy converts into strange quark matter (SQM) to achieve stability. And this QM is more stable matter. The collapse of a neutron star may lead to a strange quark star (SQS) or a hybrid star [9]. Here we consider only the structure properties of SQS. The surface density, 14 10 2 × = s ρ g cm -3 , is not the most realistic for modeling SQM star [10]. And the actual values of SQM density at zero pressure lie between 14 10 4 × to 14 10 10 × g cm -3 [11-13]. The mass- radius relation for an SQS is as M ∝ R 3 which is different from that of a neutron star. This star does not have the minimum mass. For an SQS with 1M⊙ ⩽M ⩽2M⊙, the radius is about 10 km [14, 15]. Here, we don’t want to write the physical condition for a regular and charged fluid sphere for interior solution of the gravitational field equations of a SQM star because [16] was elaborately discussed. A self-bound strange quark star belongs to a different class compact object than a conventional normal matter neutron star. The surfaces of bare strange stars and normal matter neutron stars have significant difference. The main properties of the quark surface which are strong bounding of particles abrupt density change from 3 14 10 4 - × cm g to ~ 0