Global Structure of a Black-Hole Cosmos and its Extremes

TL;DR

This paper explores the global structure of Einstein-Maxwell solutions with various parameters, revealing diverse black-hole and naked-singularity configurations in closed cosmologies, and compares these with Kastor-Traschen solutions.

Contribution

It provides a comprehensive classification of Einstein-Maxwell solutions in closed cosmologies, detailing their properties and differences from Kastor-Traschen solutions.

Findings

Identification of different solution types including black-hole and naked-singularity solutions.

Description of extreme and ultra-extreme solution properties.

Comparison with Kastor-Traschen multi-black-hole solutions.

Abstract

We analyze the global structure of a family of Einstein-Maxwell solutions parametrized by mass, charge and cosmological constant. In a qualitative classification there are: (i) generic black-hole solutions, describing a Wheeler wormhole in a closed cosmos of spatial topology $S^2\times S^1$; (ii) generic naked-singularity solutions, describing a pair of ``point" charges in a closed cosmos; (iii) extreme black-hole solutions, describing a pair of ``horned" particles in an otherwise closed cosmos; (iv) extreme naked-singularity solutions, in which a pair of point charges forms and then evaporates, in a way which is not even weakly censored; and (v) an ultra-extreme solution. We discuss the properties of the solutions and of various coordinate systems, and compare with the Kastor-Traschen multi-black-hole solutions.