Relativistic structure, stability, and gravitational collapse of charged neutron stars

Abstract

Charged stars have the potential of becoming charged black holes or even naked singularities. It is presented a set of numerical solutions of the Tolman-Oppenheimer-Volkov equations that represents spherical charged compact stars in hydrostatic equilibrium. The stellar models obtained are evolved forward in time integrating the Einstein-Maxwell field equations. It is assumed an equation of state of a neutron gas at zero temperature. The charge distribution is taken as been proportional to the rest mass density distribution. The set of solutions present an unstable branch, even with charge to mass ratios arbitrarily close to the extremum case. It is performed a direct check of the stability of the solutions under strong perturbations, and for different values of the charge to mass ratio. The stars that are in the stable branch oscillates and do not collapse, while models in the unstable branch collapse directly to form black holes. Stars with a charge greater or equal than the extreme value explode. When a charged star is suddenly discharged, it don't necessarily collapse to form a black hole. A non-linear effect that gives rise to the formation of an external shell of matter (see Ghezzi and Letelier 2005), is negligible in the present simulations. The results are in agreement with the third law of black hole thermodynamics and with the cosmic censorship conjecture.

Nonadiabatic charged spherical gravitational collapse

“…The role of charge distribution in the dynamics of such configurations is clearly exhibited in equations (36), (37), (40) and (50). In particular it is worth stressing the fact that electric charge, unlike pressure, does not always produce a "regeneration effect" (does not always increase the "active gravitational mass").…”

“…(43) in [14]. Let us now analyze in some detail the three terms on the right of (40). The first term on the right hand side of (40) represents the gravitational force.…”

“…We can couple the transport equation in the form above, (49), to the dynamical equation (40), in order to bring out the effects of dissipation on the dynamics of the collapsing sphere. For that purpose, let us substitute (49) into (40): then we obtain, after some rearrangements,…”

“…Although some of these works refer to static situations ( [3]- [5], [9,19,23,24,29,30], [32]- [34], [36,37,39,41]) there have been important efforts in describing dynamical situations too ( [6]- [8], [10]- [14], [16,17,21,22,26,40,42]). Particularly relevant for the present paper are references [14,22] and [40].…”

Realistic exact solution for the exterior field of a rotating neutron star

“…Particularly, from the numerical approach, several physical properties of NS such as energy density, inertia moments, equatorial radii and others are known through the numerical solution of the full Einstein equations, assuming different equations of state for NS and applying algorithms, specially the KomatsuEriguchi-Hashisu self consistent field-method [15] and its variants (e.g. in 2005 by Ghezzi [16], Gusakov, Yakovlev & Gnedin [17] and Berti, White, Maniopoulou & Bruni [9]. In 2004 by Berti & Stergioulas [1] and Yoshida & Eriguchi [18].…”