Inverted black holes and anisotropic collapse

Abstract

The structure of static vacuum and electrovacuum fields with the most simple symmetry is discussed within the framework of the general theory of relativity. The general electrovacuum fields with plane and pseudospherical symmetries and the special case of fields with cylindrical symmetry contain horizons with the R and T regions interchanged by comparison with the Schwarzschild solution (the “inverted black hole” structure); the horizons disappear in the presence of a massless scalar field and for small deviations from plane symmetry. The physical consequences of this structure for the simplest models of anisotropic collapse are briefly discussed. A simple method is described for constructing the Penrose diagrams for a given metric, and examples are given of the construction of new diagrams for the electrovacuum solutions with a Λ term.