Compact Cauchy horizons admit constant surface gravity

2025/06/24 by Raymond A. Hounnonkpe, E. Minguzzi, Hounnonkpe, Raymond A. +1
Earth and Planetary Sciences · Physics and Astronomy · Engineering · #Geophysics and Gravity Measurements #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2506.20004

Abstract

We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular cohomological equation. The proof uses elements of ergodic theory, Hodge theory and Riemannian flow theory. We emphasize that, remarkably, these results really require only the null energy condition, whereas previous works assumed, already in the Killing or the non-degenerate cases, the stronger dominant energy condition.

Citations

• The basic component of the mean curvature of Riemannian foliations
• Horizon Classification via Riemannian Flows
• Regularity and temperature of stationary black hole event horizons
• The Large Scale Structure of Space-Time
• The asymptotic expansion of the spacetime metric at the event horizon
• A classification theorem for compact Cauchy horizons in vacuum\n spacetimes
• On the existence of Killing fields in smooth spacetimes with a compact Cauchy horizon
• Lorentzian causality theory
• On the Greenfield-Wallach and Katok conjectures
• The four laws of black hole mechanics

Related

• Horizon Classification via Riemannian Flows
• On the existence of Killing fields in smooth spacetimes with a compact Cauchy horizon
• Null hypersurface data and ambient vector fields: Killing horizons of order zero/one
• On the existence of sections with constant surface gravity on null hypersurfaces
• Remarks on the existence of CMC Cauchy surfaces