Topological Interplay between Knots and Entangled Vortex-Membranes

TL;DR

This paper explores the topological relationship between knots and vortex-membranes in higher-dimensional space, proposing an emergent gravity framework based on zero-lattice topology and knot dynamics.

Contribution

It introduces a novel topological model linking vortex-membranes, knots, and emergent gravity within a higher-dimensional continuum framework.

Findings

Gravity emerges as a consequence of zero-lattice topology.

Knots act as topological defects influencing space-time curvature.

Zero-lattice deformation corresponds to curved space-time for knots.

Abstract

In this paper, the Kelvin wave and knot dynamics are studied on three dimensional smoothly deformed entangled vortex-membranes in five dimensional space. Owing to the existence of local Lorentz invariance and diffeomorphism invariance, in continuum limit gravity becomes an emergent phenomenon on 3+1 dimensional zero-lattice (a lattice of projected zeroes): On the one hand, the deformed zero-lattice can be denoted by curved space-time for knots; on the other hand, the knots as topological defect of 3+1 dimensional zero-lattice indicates matter may curve space-time. This work would help researchers to understand the mystery in gravity.