On Schwarzschild causality in higher dimensions

Abstract

Abstract We show that the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity I − contains the whole of the future conformal infinity I + in (2 + 1) and (3 + 1) dimensional Schwarzschild spacetimes, this property (which we call the Penrose property) does not hold for (d + 1) dimensional Schwarzschild if d > 3. We also show that the Penrose property holds for the Kerr solution in (3 + 1) dimensions, and discuss the connection with scattering theory in the presence of positive mass.