Nonsingular charged analogues of Schwarzschild’s interior solution

Abstract

The problem of finding nonsingular charged analogue of Schwarzschild's interior solutions has been reduced to that of finding a monotonically decreasing function f . The models are discussed in generality by imposing reality condition on f . It is shown that the physical solutions are possible only for surface density to central density ratio greater than or equal to 2/3 i.e. ρ a ρ 0 ≥ 2/3. The unphysical nature of solutions with linear equation state has been proved. A generalization procedure has been utilized to generalize solutions by Guilfoyle (1999). Recently found solutions by Gupta and Kumar (2005a, 2005b, 2005c are generalized by taking particular form of f and seen to have higher mass and more stable. The maximum mass is found to be 1.59482 M . The models have been found to be stable once the physical requirements are established due to mass to radius less than 4/9, total charge to total mass ratio less than 1 and redshift quite low.

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.…”

Charged analogues of Schwarzschild interior solution in terms of pressure

“…For a monotonically decreasing function f r of radius r, the expression for charge, density and pressure can be written as (Bijalwan and Gupta 2008) …”

“…Thus, regular charged perfect fluid solutions joining smoothly with the ReissnerNordstrom metric at the pressure free interface are found important in many ways. As very few physically valid exact solutions (for charged analogues of Schwarzschild interior solution) are available in literature (Bijalwan and Gupta 2008) so the approach followed by them viz. to fulfill most of the physical requirements before the solutions are actually sought, seems to be more disciplined one.…”

“…However, the charge analogues of most exact solutions, so far obtained, the numerical methods have been used to study the behavior of physical parameters from centre to boundary. Also, a number of Weyl-type solutions (Guilfoyle 1999) are known but unfortunately they can only be discussed numerically in detailed (Bijalwan and Gupta 2008). Bijalwan (2011b) applied Bijalwan (2011a) ansatz to derive charged analogues of Vaidya-Tikekar type solutions.…”

Exact solutions: neutral and charged static perfect fluids with pressure

“…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.…”