Horizons vs. singularities in spherically symmetric space-times

TL;DR

This paper classifies various horizons in static spherically symmetric space-times, analyzes their extendibility, and explores conditions under which they are singular or regular, including examples with exotic matter and cosmological models.

Contribution

It provides a comprehensive classification of horizons, necessary conditions for their extension, and examples of matter fields that produce different horizon types, including truly naked ones.

Findings

Truly naked horizons are generally non-extendable and singular.

Certain matter fields can create specific horizon types, including negative pressure fluids and scalar fields.

Horizons of order 2+ occur at infinite proper times, but communication across them remains possible.

Abstract

We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as "usual", "naked" and "truly naked" ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of matter are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.