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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.

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