On the metric bundles of axially symmetric spacetimes

TL;DR

This paper introduces the concept of metric bundles in axially symmetric spacetimes, providing explicit examples and exploring their role in understanding black holes and naked singularities through limiting frequencies of stationary observers.

Contribution

It defines metric bundles in axially symmetric geometries and demonstrates their application to solutions of Einstein equations, linking black holes and naked singularities via horizon frequencies.

Findings

Metric bundles are explicitly defined in axially symmetric spacetimes.

Horizon frequencies reveal connections between black holes and naked singularities.

Properties of metric bundles are analyzed across different frames and solutions.

Abstract

We present the definition of metric bundles in axially symmetric geometries and give explicit examples for solutions of Einstein equations. These structures have been introduced in Pugliese and Quevedo (2019) to explain some properties of black holes (BHs) and naked singularities (NSs), investigated through the analysis of the limiting frequencies of stationary observers, which are at the base of a Killing horizon definition for these black hole spacetimes. In Pugliese and Quevedo (2019), we introduced the concept of NS Killing throats and bottlenecks associated to, and explained by, the metric bundles. In particular, we proved that the horizon frequency can point out a connection between BHs and NSs. We detail this definition in general and review some essential properties of metric bundles as seen in different frames and exact solutions.