https://doi.org/10.1140/epjc/s10052-024-12919-y
Regular Article - Theoretical Physics
Horizons that gyre and gimble: a differential characterization of null hypersurfaces
1
Department of Mathematics and Statistics, Masaryk University, Building 08, Kotlářská 2, 61137, Brno, Czech Republic
2
Department of Mathematics and Statistics, UiT: The Arctic University of Norway, 9019, Tromsø, Norway
Received:
18
March
2024
Accepted:
14
May
2024
Published online:
4
June
2024
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.
© The Author(s) 2024
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