Time across null horizons
Abstract
The core message of the talk is that a globally regular definition of time is hyperboloidal. Minkowski introduced spacetime hyperboloids at the same time as spacetime in 1908. Following a circular narrative, I will review the one hundred years of time coordinates during which hyperboloidal surfaces regularly resurface. Our story follows the decades-long confusion over coordinates and covariance in general relativity, clarifying the geometric structure of the “magic sphere” in Schwarzschild spacetime and the cosmological horizon in de Sitter spacetime. Extending the basic ideas behind the construction of regular coordinates across null horizons to conformally extended, asymptotically flat spacetimes, we recognize that time across null horizons is hyperboloidal.
