Charged analogues of Schwarzschild interior solution in terms of pressure

Abstract

Recently, Bijalwan (Astrophys. Space Sci., doi: 10.1007/s10509-011-0691-0, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251-260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed some previously known and new solutions for Schwarzschild parameter u(= GM c 2 a ) ≤ 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited the range u ≤ 0.142 by considering pressure p = p(ω) and2 to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface red shift z s ≤ 0.181, central red shift z c ≤ 0.282, mass to radius ratio M/a ≤ 0.149, total charge to total mass ratio e/M ≤ 0.807 and satisfy Andreasson's (Commun. Math. Phys. 288, 715-730, 2009) stability condition. Red-shift, velocity of sound and p/c 2 ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found to be 1.512 M with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn't have neutral counter part. These solutions completely describe interior of a stable Neutron star N. Bijalwan ( ) FreeLancer, c/o Sh. Rajkumar Bijalwan, Nirmal Baag, Part A,

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

“…Known applicable analytic solutions include [4,5,22]: In contrast, as far the literature is concerned known to the present authors, the charged analogs of Tolman's models (V-VI) obtained in [95][96][97][98][99][100][101] are not physically viable in the description of compact astrophysical objects as regards the infinite values of the central density and pressure. Though the Schwarzschild constant density solution is physically unrealistic, the charged analogs, obtained in [56,[102][103][104], and the charged analog of the Matese and Whitman solution, obtained in [105], may be relevant in the description of self-bound electrically charged strange quark stars. Charged analogs of the Tolman IV and VII models [106][107][108]), as the neutral ones, exhibit the physical features required for the construction of a physically realizable relativistic compact stellar structure.…”

Exact solutions: neutral and charged static perfect fluids with pressure

“…So, none of the charged fluid solutions with (2.8b) has a well behaved neutral counter part in present case. Some of the special cases are discussed in Bijalwan (2011bBijalwan ( , 2011cBijalwan ( , 2011d. Bijalwan (2011d) showed that these solutions mimic classical electron model.…”

“…Case A: Consider the solution derived by Bijalwan (2011c). The various parameters are written as e −λ = 1 − r 2 /R 2 , e υ = y 2 ,…”

“…Also, the charge generalization of the incompressible Schwarzschild interior spheres i.e. with constant non-gravitational energy density (T 4 4 ) found by Florides (1983), Guilfoyle (1999), Gupta and Kumar (2005), Bijalwan and Gupta (2008), Bijalwan (2011c). The charged fluids obtained by Gupta and Kumar (2005), Bijalwan and Gupta (2008), Bijalwan (2011bBijalwan ( , 2011c and Pant et al (2010a) do not admit their weel behaved neutral counterpart.…”

“…Many of the authors electrified the well known exact solutions as seed solutions e.g Kuchowicz solutions (1968) by Nduka (1977), Tolman solution (1939 by Cataldo and Mitskievic (1992), Durgapal and Fuloria solution (1985) by Maurya (2010a), Heintzmann's (1969) solution by Pant et al (2010b), Durgapal (1982 by Gupta and Maurya (2010b, 2011), Kuchowicz solutions (1967 by Gupta and Maurya (2010c), Buchdahl (1959) by Gupta and Kumar (2005), Bijalwan and Gupta (2008), Bijalwan (2011bBijalwan ( , 2011c etc. These coupled solutions completely describe interior of the Neutron star or pulsar with charge matter.…”