Some global, analytical, and topological properties of regular black holes

Abstract

In this work, we study regular black holes from a global perspective, looking to evade some of the well-known singularity theorems by using their “reverses.” Then, model geometries for the slices of typical spherically symmetric, (locally) static four-dimensional regular black hole solutions are described from both an analytical and a topological point of view. While the finiteness of both the scalar and Kretchmann curvature of the slices around the regular center determines the geometry of the core, the positive answer to the Poincaré conjecture assures that, under two assumptions, its topology is that of a three-sphere. However, in general, the cores are shown to be S3, H3, R×S1, or S1×S2, depending on whether de Sitter, anti–de Sitter, Nariai, or Bertotti-Robinson geometries are employed to describe the slices at the regular center. Then, a description of the aforementioned slices in terms of Seifert fiber spaces is given in order to show that the Euler characteristic of the bundle can be used to track the transition between the core of the regular black hole and the rest of the slices in most of the cases considered in the literature. After Geroch and Tipler’s theorems are employed to study the consequences of topology change on regular black hole spacetimes, we show that Borde and Vilenkin’s singularity theorem is used to restrict their possible types. We end by noting that Nariai cores can be safely used to construct regular black holes without topology changes.