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The deformation retract is, by definition, a homotopy between a retractionand the identity map. We show that applying this topological concept toRicci-flat wormholes/black holes implies that such objects can get deformed andreduced to lower dimensions. The homotopy theory can provide a rigorous proofto the existence of black holes/wormholes deformations and explain thetopological origin. The current work discusses such possible deformations anddimensional reductions from a global topological point of view, it alsorepresents a new application of the homotopy theory and deformation retract inastrophysics and quantum gravity.

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