Horizons that gyre and gimble: a differential characterization of null hypersurfaces

• Published in: The European physical journal. C, Particles and fields Vol. 84; no. 6; pp. 561 - 18
• Main Authors: Blitz, Samuel, McNutt, David
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 04.06.2024; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Conformal mapping; Differential calculus; Elementary Particles; Geometry; Hadrons; Heavy Ions; Hyperspaces; Invariants; Manifolds (mathematics); Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory
• DOI: 10.1140/epjc/s10052-024-12919-y
• ISSN: 1434-6052; 1434-6044

Motivated by the thermodynamics of black hole solutions conformal to stationary solutions, we study the geometric invariant theory of null hypersurfaces. It is well-known that a null hypersurface in a Lorentzian manifold can be treated as a Carrollian geometry. Additional structure can be added to this geometry by choosing a connection which yields a Carrollian manifold. In the literature various authors have introduced Koszul connections to study the study the physics on these hypersurfaces. In this paper we examine the various Carrollian geometries and their relationship to null hypersurface embeddings. We specify the geometric data required to construct a rigid Carrollian geometry, and we argue that a connection with torsion is the most natural object to study Carrollian manifolds. We then use this connection to develop a hypersurface calculus suitable for a study of intrinsic and extrinsic differential invariants on embedded null hypersurfaces; motivating examples are given, including geometric invariants preserved under conformal transformations.