Black holes and quasiblack holes in Einstein-Maxwell theory

Continuous sequences of asymptotically flat solutions to the Einstein-Maxwell equations describing regular equilibrium configurations of ordinary matter can reach a black hole limit. For a distant observer, the spacetime becomes more and more indistinguishable from the metric of an extreme Kerr-Newman black hole outside the horizon when approaching the limit. From an internal perspective, a still regular but non-asymptotically flat spacetime with the extreme Kerr-Newman near-horizon geometry at spatial infinity forms at the limit. Interesting special cases are sequences of Papapetrou-Majumdar distributions of electrically counterpoised dust leading to extreme Reissner-Nordstrom black holes and sequences of rotating uncharged fluid bodies leading to extreme Kerr black holes.