# Topology Change of Black Holes

## TL;DR

This paper investigates the topological evolution of black hole event horizons using Morse theory, revealing constraints on handle attachments and implications for black hole formation topology.

## Contribution

It introduces a classification of handle attachments in black hole topologies and demonstrates constraints on their evolution, including the non-axisymmetry of certain horizon formations.

## Key findings

- Only black handles appear in real black hole spacetimes.
- The exterior spatial section remains connected during evolution.
- Certain horizon topologies require non-axisymmetric formation.

## Abstract

The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain constraints on the nature of black hole topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of an exterior of the black hole region is always connected. As a corollary, it is shown that the formation of a black hole with an S**(n-2) x S**1 horizon from that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat space-times.