The relationship between the critical sets and Morse codes of electrically charged knots

Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. From the standpoint of both physics and knot theory, it is natural to try to understand the critical points of the potential and their behavior. By taking successive preimages of regular potential values, we get an $N-$tuple of compact orientable surfaces, whose genera we define as the Morse code. We relate the topological data of the critical set to the Morse code. We show that critical points of index $1$ correspond to increases in successive terms in the Morse code, whilst critical points of index $2$ correspond to decreases. Our theorem is proven with Morse theory and techniques from geometric topology. keywords: knot theory, electrostatics, Morse theory, Morse code, dynamical systems, geometric topology