Concepts of equivalence abound in the physical sciences, more so in the study of high energy elementary particles. However, it can be conjectured that the intrinsic angular momentum called the spin is fundamentally not equivalent to the concept of topologically closed volume of space-time. This potentially damaging (to other well established physical theories) concept of nonequivalence poses the question whether experiments can simultaneously detect spin zero elementary particles like the Higgs boson and also the appearance of spontaneous spherically symmetric topology of genus zero for a closed volume of space-time. In other words, can it be physically possible to detect the spin of a space-time singularity?

On the other hand, the general relativity of black holes presented the no-hair theorem which states that a black hole always has three major characteristics: mass, electric charge, and spin. Attributing these properties would theoretically suggest that black holes can never be considered as elementary particles or as space-time singularities. Furthermore, spinning black holes are theoretically nonspherical while spherical ones are always nonrotating. The former is described by the Kerr and the Kerr-Newman models while the latter is described by the Schwarzschild model. Property of nonequivalence between spin and genus zero structures of space-time can be described by the rational function SV=V-S where S denotes the spin quantum number and V the quantum volume of space-time. If S=1/2 then V=1 and if S=0 then V=0. Nonetheless, S can be 1 if and only if V=infinity. Moreover, if S=2 then V=-2. This represents the spin of the hypothetical graviton and suggesting that its space-time volume is negative if defined as oriented volumes of four dimensional vector or tensor space-time domains which can be represented by symmetric singular Hadamard matrices.