Two kinds of extreme black holes and their classification

TL;DR

This paper proposes a classification of extreme black holes based on their topological configurations, specifically using the Euler characteristic to distinguish two types.

Contribution

It introduces a novel topological classification scheme for extreme black holes using Euler characteristic as the key parameter.

Findings

Two types of extreme black holes identified by Euler characteristic

Euler characteristic distinguishes four-dimensional and two-dimensional holes

Classification scheme based on topological properties

Abstract

According to different topological configurations, we suggest that there are two kinds of extreme black holes in the nature. We find that the Euler characteristic plays an essential role to classify these two kinds of extreme black holes. For the first kind of extreme black holes, Euler characteristic is zero, and for the second kind, Euler characteristic is two or one provided they are four dimensional holes or two dimensional holes respectively.