Potential Carroll Structures and Special Carrollian Manifolds

TL;DR

This paper introduces potential Carroll structures as a new intrinsic geometric framework for null hypersurfaces in Lorentzian manifolds, motivated by flat-space holography, and explores their relation to special Carrollian manifolds.

Contribution

It proposes potential Carroll structures as a novel intrinsic geometry for null hypersurfaces and examines their connection to special Carrollian manifolds.

Findings

Potential Carroll structures provide an intrinsic description of null hypersurfaces.

The relationship between potential Carroll structures and special Carrollian manifolds is analyzed.

The framework may be useful in contexts involving conformal isometries.

Abstract

It is well-known that unlike space-like and time-like hypersurfaces, null hypersurfaces in Lorentzian manifolds do not naturally inherit an affine connection from the spacetime in which they are embedded. On the other hand, recent developments in flat-space holography motivate the study of the intrinsic geometry of null hypersurfaces such as null infinity and black hole event horizons. Here we initiate the study of potential Carroll structures, a candidate for an intrinsic description of null hypersurfaces which may be particularly useful in settings where conformal isometries are of interest, and we explore their relationship to another such candidate intrinsic geometry, the special Carrollian manifolds.