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Thick shells and stars in Majumdar-Papapetrou general relativity. (English) Zbl 1093.83017
Summary: We find an exact solution for the Majumdar-Papapetrou system, a spherically symmetric charged thick shell, with mass \(m\), charge \(q=m\), outer radius \(r_0\), and inner radius \(r_i\). This solution consists of three regions: an inner Minkowski region, a middle region with extreme charged dust matter, and an outer Reissner-Nordström region. The regions are matched continuously with the usual junction conditions for boundary surfaces. For a vanishing inner radius, one obtains a Bonnor star, whereas for vanishing thickness, one obtains an infinitesimally thin shell. For a sufficiently high mass of the thick shell or a sufficiently small outer radius, it forms an extreme Reissner-Nordström quasi-black hole, i.e., a charged star whose gravitational properties are virtually indistinguishable from a true extreme black hole. This quasi-black hole has no hair and contains a naked horizon, meaning that the Riemann tensor at the horizon on an infalling test particle diverges. At the critical value, when the mass is equal to the outer radius, \(m=r_0\), there is no smooth manifold. Above the critical value, when \(m>r_0\), there is no stable solution, the shell collapses into a singularity. Systems with \(m<r_0\) are neutrally stable. Many of their properties are similar to those of gravitational monopoles.

83C50 Electromagnetic fields in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory