Time in Conformal General Relativity
2015 Midwest Relativity Meeting, CIERA Northwestern University
Gravity theories based on the conformal group give general relativity augmented by local dilatational covariance. In one of these theories, biconformal gravity, the dimension of the original space doubles, giving a symplectic manifold with conformal general relativity on a lagrangian submanifold.
The restriction of the Killing form to the biconformal space is non-degenerate and signature-changing. This opens several possibilities, from time arising only within solutions to a Euclidean gravity theory, to novel approaches to the AdS/CFT correspondence, or the natural emergence of an SO(n) Yang-Mills field on gravitating spacetime. We briefly discuss some of our investigations into these options.
Wheeler, James Thomas, "Time in Conformal General Relativity" (2015). All Physics Faculty Publications. Paper 2024.