Deformation Retract and Folding of the 5D Schwarzchild Field

TL;DR

This paper explores deformation retracts and folding in 5D Schwarzschild space using Lagrangian equations, establishing relations between these topological features and energy conservation in higher dimensions.

Contribution

It introduces new types of deformation retracts in 5D Schwarzschild space and relates folding to these retracts, extending energy conservation concepts to five dimensions.

Findings

Deformation retracts of 5D Schwarzschild space are characterized.

Folding is related to deformation retracts in this space.

Energy conservation relation is extended to 5D case.

Abstract

In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.