Hyperbolic energy and Maskit gluings

Piotr T. Chruściel; Erwann Delay; Raphaela Wutte

doi:10.48550/arXiv.2112.00095

Hyperbolic energy and Maskit gluings

Piotr T. Chruściel (Corresponding author), Erwann Delay (Corresponding author), Raphaela Wutte (Corresponding author)

Gravitational Physics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.

Original language	English
Pages (from-to)	1333-1403
Number of pages	71
Journal	Advances in Theoretical and Mathematical Physics
Volume	27
Issue number	5
DOIs	https://doi.org/10.48550/arXiv.2112.00095 https://doi.org/10.4310/ATMP.2023.v27.n5.a2
Publication status	Published - 15 Jul 2024

Funding

We are grateful to Michael Anderson, Greg Galloway, Colin Guillarmou, Jack Lee, Yanyan Li, Rafe Mazzeo, Bruno de Oliveira and Laurent V\u00E9ron for useful discussions. PTC was supported in part by the Austrian Science Fund (FWF) under project P29517-N27 and by the Polish National Center of Science (NCN) 2016/21/B/ST1/00940. Part of this research was performed while PTC was visiting the Institute for Pure and Applied Mathematics (IPAM) at UCLA, which is supported by the National Science Foundation (Grant No. DMS-DMS-1925919). ED was supported by the grant ANR-17-CE40-0034 (project CCEM) and by the grant ANR-23-CE40-0010-02 (project EINSTEIN-PPF) of the French National Research Agency. RW was supported by the Austrian Science Fund FWF under the Doctoral Program W1252-N27 Particles and Interactions. RW thanks the University of Amsterdam for hospitality during the completion of this project. C(xA) = 1(DADBDAu)(DBu) 6() +RAB\u22121R\u02DAhAB DuDu .AB 12 2 Acknowledgements. We are grateful to Michael Anderson, Greg Galloway, Colin Guillarmou, Jack Lee, Yanyan Li, Rafe Mazzeo, Bruno de Oliveira and Laurent V\u00E9ron for useful discussions. PTC was supported in part by the Austrian Science Fund (FWF) under project P29517-N27 and by the Polish National Center of Science (NCN) 2016/21/B/ST1/00940. Part of this research was performed while PTC was visiting the Institute for Pure and Applied Mathematics (IPAM) at UCLA, which is supported by the National Science Foundation (Grant No. DMS-DMS-1925919). ED was supported by the grant ANR-17-CE40-0034 (project CCEM) and by the grant ANR-23-CE40-0010-02 (project EINSTEIN-PPF) of the French National Research Agency. RW was supported by the Austrian Science Fund FWF under the Doctoral Program W1252-N27 Particles and Interactions. RW thanks the University of Amsterdam for hospitality during the completion of this project.

Austrian Fields of Science 2012

101006 Differential geometry
103028 Theory of relativity
103012 High energy physics

Access to Document

Cite this

@article{553f124fd85f450599b8b21cdcb904b7,

title = "Hyperbolic energy and Maskit gluings",

abstract = "We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.",

author = "Chru{\'s}ciel, \{Piotr T.\} and Erwann Delay and Raphaela Wutte",

year = "2024",

month = jul,

day = "15",

doi = "10.48550/arXiv.2112.00095",

language = "English",

volume = "27",

pages = "1333--1403",

journal = "Advances in Theoretical and Mathematical Physics",

issn = "1095-0761",

publisher = "INT PRESS BOSTON, INC",

number = "5",

}

TY - JOUR

T1 - Hyperbolic energy and Maskit gluings

AU - Chruściel, Piotr T.

AU - Delay, Erwann

AU - Wutte, Raphaela

PY - 2024/7/15

Y1 - 2024/7/15

N2 - We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.

AB - We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.

UR - https://www.scopus.com/pages/publications/85200889373

U2 - 10.48550/arXiv.2112.00095

DO - 10.48550/arXiv.2112.00095

M3 - Article

AN - SCOPUS:85200889373

SN - 1095-0761

VL - 27

SP - 1333

EP - 1403

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

IS - 5

ER -

Hyperbolic energy and Maskit gluings

Abstract

Funding

Austrian Fields of Science 2012

Access to Document

Other files and links

Fingerprint

Elliptische Probleme in der Allgemeinen Relativitätstheorie

Particles and Interactions

Cite this

Hyperbolic energy and Maskit gluings

Abstract

Funding

Austrian Fields of Science 2012

Access to Document

Other files and links

Fingerprint

Projects

Elliptische Probleme in der Allgemeinen Relativitätstheorie

Particles and Interactions

Cite this