Interacting with the Fifth Dimension

The use of the scalar-Einstein field equations and their solutions seems to have gone through four, perhaps related, stages. In the first stage [1] solutions were sought which it was hoped would represent an elementary particle such as a meson. How the scalar field decays from such solutions might effect the Yukawa potential has been discussed by Roberts [2]. In the second stage it was noticed that most scalar-Einstein solutions do not have event horizons. It was shown that no event horizons happen under fairly general conditions in the static case [3]. In the nonstatic case there are imploding solutions which create curvature singularities out of nothing [4,5], these examples have no overall mass, but there is a mass in the corresponding conformalscalar solutions [6]. In the third stage exact scalar-Einstein solutions where found to be critical cases in the numerical study of stellar collapse [7]. In the fourth stage exact scalar-Einstein solutions were canonically quantized [8].