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@article{2421887,
author = {Blitz, Samuel Harris and Mcnutt, David},
article_location = {New York},
article_number = {6},
doi = {http://dx.doi.org/10.1140/epjc/s10052-024-12919-y},
keywords = {General Relativity and Quantum Cosmology; Differential Geometry},
language = {eng},
issn = {1434-6044},
journal = {European Physical Journal C},
title = {Horizons that gyre and gimble: a differential characterization of null hypersurfaces},
url = {https://link.springer.com/article/10.1140/epjc/s10052-024-12919-y},
volume = {84},
year = {2024}
}
TY - JOUR
ID - 2421887
AU - Blitz, Samuel Harris - Mcnutt, David
PY - 2024
TI - Horizons that gyre and gimble: a differential characterization of null hypersurfaces
JF - European Physical Journal C
VL - 84
IS - 6
SP - 1-18
EP - 1-18
PB - Springer
SN - 14346044
KW - General Relativity and Quantum Cosmology
KW - Differential Geometry
UR - https://link.springer.com/article/10.1140/epjc/s10052-024-12919-y
N2 - 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.
ER -
BLITZ, Samuel Harris and David MCNUTT. Horizons that gyre and gimble: a differential characterization of null hypersurfaces. \textit{European Physical Journal C}. New York: Springer, 2024, vol.~84, No~6, p.~1-18. ISSN~1434-6044. Available from: https://dx.doi.org/10.1140/epjc/s10052-024-12919-y.
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