On the existence of deformations and dimensional reduction in wormholes and black holes

TL;DR

This paper explores how topological homotopy and deformation retract concepts suggest that Ricci-flat wormholes and black holes can undergo deformations and dimensional reductions, offering a new perspective in astrophysics and quantum gravity.

Contribution

It introduces a novel application of homotopy theory to demonstrate possible deformations and dimensional reductions of black holes and wormholes from a topological standpoint.

Findings

Deformations of black holes and wormholes are topologically plausible.

Homotopy theory provides a rigorous framework for these deformations.

Dimensional reduction of such objects can be explained through topological methods.

Abstract

The deformation retract is, by definition, a homotopy between a retraction and the identity map. We show that applying this topological concept to Ricci-flat wormholes/black holes implies that such objects can get deformed and reduced to lower dimensions. The homotopy theory can provide a rigorous proof to the existence of black holes/wormholes deformations and explain the topological origin. The current work discusses such possible deformations and dimensional reductions from a global topological point of view, it also represents a new application of the homotopy theory and deformation retract in astrophysics and quantum gravity.