Cosmic cloaking of rich extra dimensions

We present arguments that show why it is difficult to see rich extra dimensions in the universe. Conditions are found where significant size and variation of the extra dimensions in a Kaluza–Klein compactification lead to a black hole in the lower-dimensional theory. The idea is based on the hoop conjecture concerning black hole existence, as well as on the observation that dimensional reduction on macroscopically large, twisted, or highly dynamical extra dimensions contributes positively to the energy density in the lower-dimensional theory and can induce gravitational collapse. A threshold for the size is postulated on the order of [Formula: see text][Formula: see text]m, whereby extra dimensions of length above this level must lie inside black holes, thus cloaking them from the view of outside observers. The threshold depends on the size of the universe, leading to speculation that in the early stages of evolution truly macroscopic and large extra dimensions would have been visible.