Thick shells and stars in Majumdar-Papapetrou general relativity.

*(English)*Zbl 1093.83017Summary: 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.