Extremely electrically charged compact stars and formation of quasi black holes

Full text: We extend here the study performed some years ago by some of us on the the effect of electric charge in compact stars by assuming that the charge distribution is proportional to the mass density (Phys. Rev. D 68, 084004 (2003)). As well known, the pressure and the density of the matter inside compact stars are large, and the gravitational field is intense, indicating that electric charge and a strong electric field can also be present. Using the relativistic hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff equation, modified in order to include electric charge, we perform a detailed numerical study of the effect of electric charge modelling the star by a charged perfect fluid which satisfies different equations of state. We compare the results using a polytropic equation of state as done in the above mentioned work, of the form (I) p Kρ1+1/n, with the results obtained using an equation of state of the form (II) p = Kρo1+/n, with ρ = p0c2 + np, where ρ0 is the proper matter density and ρ is the energy density. This second form of equation of state is more appropriate in the regime of very high energy densities, as the we consider in the present work. In fact, we verify that in the regime of low densities and pressure, both of the equations (I) and (II) yield approximately the same results. We then investigate the regime of extremely charged stars in both cases. It is found that for a variety of central densities there may be equilibrium solutions were the the charge is very close the the mass of the star (in geometrical units). In some particular cases, the radius of the star is very close to the event horizon, indicating that the star is on the verge of becoming a quasi black hole. The main physical properties, such as the sound speed end the energy conditions, of the stars in the extremal regime is also investigated. It is found that for a very large range of parameters there are equilibrium configurations that satisfy the required physical conditions for relativistic stars. (author)