You Cannot Press Out the Black Hole

TL;DR

This paper proves that certain topological transformations of black holes, such as pressing out a spherical black hole into a ring-shaped one, are impossible, establishing fundamental topological constraints.

Contribution

It introduces a new topological prohibition law for black hole transformations and extends no-bifurcation theorems to include topology change restrictions.

Findings

Pressing out a spherical black hole into a ring shape is impossible.

A general prohibition law for black hole topology change is established.

Includes a version of no-bifurcation theorems for black holes.

Abstract

It is shown that a ball-shaped black hole region homeomorphic with D**n cannot be pressed out, along whichever axis penetrating the black hole region, into a black ring with a doughnut-shaped black hole region homeomorphic with S**1 x D**(n-1). A more general prohibition law for the change of the topology of black holes, including a version of no-bifurcation theorems for black holes, is given.