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

J 2024

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

BLITZ, Samuel Harris and David MCNUTT

Basic information

Original name

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

Authors

BLITZ, Samuel Harris (840 United States of America, belonging to the institution) and David MCNUTT

Edition

European Physical Journal C, New York, Springer, 2024, 1434-6044

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL URL

Impact factor

Impact factor: 4.400 in 2022

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1140/epjc/s10052-024-12919-y

UT WoS

001239390500012

Keywords in English

General Relativity and Quantum Cosmology; Differential Geometry

Abstract

V originále

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.

Links

EH22_010/0007541, research and development project

Name: MSCAfellow6_MUNI

GA22-00091S, research and development project

Name: Geometrické struktury, invariance a diferenciální rovnice se vztahem k matematické fyzice (Acronym: GSIDRVMF)

Investor: Czech Science Foundation

Citovat

BLITZ, Samuel Harris and David MCNUTT. Horizons that gyre and gimble: a differential characterization of null hypersurfaces. 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.

@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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