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A family of charge analogue of Durgapal solution

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We obtain a new parametric class of exact solutions of Einstein–Maxwell field equations which are well behaved. We present a charged super-dense star model after prescribing particular forms of the metric potential and electric intensity. The metric describing the super dense stars joins smoothly with the Reissner–Nordstrom metric at the pressure free boundary. The electric density assumed is \(\frac{E^{2}}{c_{1}} = \frac{Kx}{2}(1 + x)^{n}(1 + 6x)^{\frac{2}{3}}\) where n may take the values 0,1,2,3,4 and so on and K is a positive constant. For n=0,1 we rediscover the solutions by Gupta and Maurya (Astrophys. Space Sci. 334(1):155, 2011) and Fuloria et al. (J. Math. 2:1156, 2011) respectively. The solution for n=2 have been discussed extensively keeping in view of well behaved nature of the charged solution of Einstein–Maxwell field equations. The solution for n=3 and n=4 can be also studied likewise. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982). The outmarch of pressure, density, pressure-density ratio and the velocity of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Neutron stars and Pulsars.

By assuming the surface density ρ b =2×1014 g/cm3 (Brecher and Caporaso in Nature 259:377, 1976), corresponding to K=12 with X=0.1, the resulting well behaved model has the mass M=2.12M , radius R b ≈16.07 km and moment of inertia I=4.95×1045 g cm2; for K=8 with X=0.1, the resulting well behaved model has the mass M=1.50M , radius R b ≈16.78 km and moment of inertia I=3.68×1045 g cm2. These values of masses and moment of inertia are found to be consistent with other models of Neutron stars and Pulsars available in the literature and are applicable for the Crab Pulsars.

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Authors acknowledge their gratitude to Dr. Neeraj Pant (Associate Professor) Maths Deptt., National Defense Academy Khadakwasla, Pune for his stimulating discussions and motivation. Authors are also grateful to the referee for pointing out the errors in original manuscript and making constructive suggestions.

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Correspondence to Pratibha Fuloria.

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Fuloria, P., Tewari, B.C. A family of charge analogue of Durgapal solution. Astrophys Space Sci 341, 469–475 (2012).

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