A family of well behaved charge analogues of Durgapal's perfect fluid exact solution in general relativity

TL;DR

This paper introduces a new family of exact solutions for charged perfect fluid stars in general relativity, modeling superdense stars like the Crab pulsar and providing insights into their mass, radius, and moments of inertia.

Contribution

It presents a novel family of well-behaved, charged perfect fluid solutions in Einstein-Maxwell equations, applicable for modeling superdense stars with realistic parameters.

Findings

Models the Crab pulsar with mass 1.3679 solar masses and radius 13.21 km.

Predicts maximum mass of superdense objects as 4.7487 solar masses.

Provides moments of inertia for specific pulsars consistent with observations.

Abstract

This paper presents a new family of interior solutions of Einstein-Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, 2.5E17 kg/m3. By this model we obtain the mass of the Crab pulsar, MCrab 1.3679 solar mass and radius 13.21 km, constraining the moment of inertia > 1.61E38 kg m2 for the conservative estimate of Crab nebula of 2 solar mass . And MCrab = 1.9645 solar mass with radius 14.38 km constraining the moment of inertia > 3.04E38 kg m2 for the newest estimate of Crab nebula mass, 4.6 solar mass. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I_A = 1.4285E38 kg m2 and I_B=1.3647E38 kg m2 respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, Mmax, 4.7487 solar mass with radius R(Mmax) = 15.24 km, surface redshift 0.9878, charge 7.91E20 C, and central density 4.31 times nuclear density.