Shahn Majid
Quantum and classical geodesic flows on a black-hole background
I describe a recent formulation with Beggs of generally covariant quantum mechanics, which in the Schrödinger picture amounts to wave functions on spacetime governed by a proper time Klein-Gordon flow. Recent work with K. Kumar extends results previously found on the exterior of a black-hole to inside the black hole, finding now a discrete mass spectrum of `atomic’ solutions of the Klein-Gordon equations, where the spectrum depends mildly on the regularisation of the theory by cutting off the domain to just inside the horizon. We also show with Kumar how the theory applies to classical geodesics on a black-hole background viewed as a density flow and, hypothetically, as an underlying wave-function amplitude flow. We show that two `bump’ wave functions of opposite sign can collide to form a dipole with a different density profile from two density bumps merging when they collide. If time, I will also describe some results with Beggs for Klein-Gordon flows on FLRW cosmological backgrounds.
