Geometric inequality for axisymmetric black holes with angular momentum
In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating blac...
Saved in:
| Published in | Classical and quantum gravity Vol. 42; no. 6; pp. 65022 - 65040 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
IOP Publishing
21.03.2025
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0264-9381 1361-6382 |
| DOI | 10.1088/1361-6382/adb82a |
Cover
| Abstract | In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating black hole is defined in terms of the momentum constraint, without any reference to a stationary Killing vector field. The momentum constraint is then shown to be equivalent to the dynamics of a two-dimensional steady compressible fluid flow governed by a quasi-conformal mapping. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose-type inequality for black holes with angular momentum. |
|---|---|
| AbstractList | In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating black hole is defined in terms of the momentum constraint, without any reference to a stationary Killing vector field. The momentum constraint is then shown to be equivalent to the dynamics of a two-dimensional steady compressible fluid flow governed by a quasi-conformal mapping. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose-type inequality for black holes with angular momentum. |
| Author | Yan, Ruodi Gao, Sijie Feng, Xuefeng Lau, Yun-Kau Yau, Shing-Tung |
| Author_xml | – sequence: 1 givenname: Xuefeng orcidid: 0000-0002-3195-6924 surname: Feng fullname: Feng, Xuefeng organization: Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) , Shanghai 200433, People’s Republic of China – sequence: 2 givenname: Ruodi orcidid: 0000-0002-7129-9826 surname: Yan fullname: Yan, Ruodi organization: Beijing Normal University Department of Physics, Beijing 100875, People’s Republic of China – sequence: 3 givenname: Sijie orcidid: 0000-0002-8179-8514 surname: Gao fullname: Gao, Sijie organization: Beijing Normal University Department of Physics, Beijing 100875, People’s Republic of China – sequence: 4 givenname: Yun-Kau orcidid: 0000-0002-9097-7346 surname: Lau fullname: Lau, Yun-Kau organization: Chinese Academy of Sciences Institute of Applied Mathematics, Morningside Center of Mathematics, LSSC, Academy of Mathematics and System Science, 55, Zhongguancun Donglu, Beijing 100190, People’s Republic of China – sequence: 5 givenname: Shing-Tung surname: Yau fullname: Yau, Shing-Tung organization: Tsinghua University Yau Mathematical Sciences Center, Beijing 100084, People’s Republic of China |
| BookMark | eNp1kM1OwzAQhC1UJNLCnaMfgFCvnR_niCooSJW4wNlapzZ1SeJiJ4K-PY1SceO00u5-o5mZk1nnO0PILbB7YFIuQRSQFkLyJW615HhBkr_VjCSMF1laCQlXZB7jnjEACTwh67XxremDq6nrzNeAjeuP1PpA8cfFY3u-6QbrT7rzjYn02_U7it3H0GCg7Ynu-qG9JpcWm2huznNB3p8e31bP6eZ1_bJ62KQ1F6JPt5BbQG6rmoMwTGNlIGOVzkutpcxFVgJKlMJsM1kVJTJdIJRlZY3WudQoFoRNunXwMQZj1SG4FsNRAVNjEWpMrcbUairihNxNiPMHtfdD6E4G_3__BZjKYok |
| CODEN | CQGRDG |
| Cites_doi | 10.1103/PhysRevLett.25.1596 10.1088/1361-6382/aaa0a6 10.4310/jdg/1090349447 10.1088/0264-9381/29/7/073001 10.1007/BF01444701 10.1007/s002200050159 10.1088/0264-9381/26/19/193001 10.1007/s10714-019-2600-8 10.4310/jdg/1207834657 10.4310/jdg/1090349428 10.1088/0264-9381/23/23/016 10.1007/s002200050700 10.1086/150635 10.1007/BF01208277 10.1007/BF01880262 10.1088/0264-9381/4/2/011 10.1088/0264-9381/2/2/012 |
| ContentType | Journal Article |
| Copyright | 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved. |
| Copyright_xml | – notice: 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved. |
| DBID | AAYXX CITATION |
| DOI | 10.1088/1361-6382/adb82a |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Physics |
| EISSN | 1361-6382 |
| ExternalDocumentID | 10_1088_1361_6382_adb82a cqgadb82a |
| GrantInformation_xml | – fundername: National Key Research and Development Program of China grantid: Grant No. 2021YFC2202501 – fundername: National Natural Science Foundation of China grantid: 11775022 and 11873044 funderid: http://dx.doi.org/10.13039/501100001809 |
| GroupedDBID | -DZ -~X 1JI 29B 4.4 5B3 5GY 5PX 5VS 5ZH 6J9 7.M 7.Q AAGCD AAGID AAJIO AAJKP AATNI ABCXL ABHWH ABJNI ABQJV ABVAM ACAFW ACGFO ACGFS ACHIP AEFHF AENEX AFYNE AKPSB ALMA_UNASSIGNED_HOLDINGS AOAED ASPBG ATQHT AVWKF AZFZN CBCFC CEBXE CJUJL CRLBU CS3 DU5 EBS EDWGO EMSAF EPQRW EQZZN IHE IJHAN IOP IZVLO KOT LAP N5L N9A P2P PJBAE R4D RIN RNS RO9 ROL RPA SY9 TN5 W28 XPP ZMT AAYXX ADEQX AEINN CITATION |
| ID | FETCH-LOGICAL-c233t-d15f1a2f9c213e0ba9e1409b57bb8853471a8a83ed48967a0b6a1779febb58ba3 |
| IEDL.DBID | IOP |
| ISSN | 0264-9381 |
| IngestDate | Wed Oct 01 06:50:39 EDT 2025 Tue Mar 11 23:40:26 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| License | This article is available under the terms of the IOP-Standard License. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c233t-d15f1a2f9c213e0ba9e1409b57bb8853471a8a83ed48967a0b6a1779febb58ba3 |
| Notes | CQG-112309.R1 |
| ORCID | 0000-0002-9097-7346 0000-0002-7129-9826 0000-0002-8179-8514 0000-0002-3195-6924 |
| PageCount | 19 |
| ParticipantIDs | iop_journals_10_1088_1361_6382_adb82a crossref_primary_10_1088_1361_6382_adb82a |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-21 |
| PublicationDateYYYYMMDD | 2025-03-21 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-21 day: 21 |
| PublicationDecade | 2020 |
| PublicationTitle | Classical and quantum gravity |
| PublicationTitleAbbrev | CQG |
| PublicationTitleAlternate | Class. Quantum Grav |
| PublicationYear | 2025 |
| Publisher | IOP Publishing |
| Publisher_xml | – name: IOP Publishing |
| References | James (cqgadb82abib11) 1970; 162 Bray (cqgadb82abib9) 2004 Anglada (cqgadb82abib10) 2018; 35 Bray (cqgadb82abib3) 2001; 59 Mars (cqgadb82abib8) 2009; 26 Dain (cqgadb82abib7) 2012; 29 Shaw (cqgadb82abib13) 1985; 2 Penrose (cqgadb82abib1) 1982; vol 102 Christodoulou (cqgadb82abib4) 1970; 25 Witten (cqgadb82abib12) 1981; 80 Penrose (cqgadb82abib21) 1984; 2 Lau (cqgadb82abib23) 2020 Penrose (cqgadb82abib20) 1984 Khuri (cqgadb82abib15) 2019; 51 Atiyah (cqgadb82abib18) 1975; vol 77 Sen (cqgadb82abib17) 1982; 21 Zhang (cqgadb82abib14) 1999; 206 RPAC Newman (cqgadb82abib16) 1987; 4 Dain (cqgadb82abib5) 2006; 23 Dain (cqgadb82abib6) 2008; 79 Herzlich (cqgadb82abib19) 1997; 188 Huisken (cqgadb82abib2) 2001; 59 Bär (cqgadb82abib22) 1992; 293 |
| References_xml | – volume: 25 start-page: 1596 year: 1970 ident: cqgadb82abib4 article-title: Reversible and irreversible transformations in black-hole physics publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.25.1596 – volume: 35 year: 2018 ident: cqgadb82abib10 article-title: Penrose-like inequality with angular momentum for minimal surfaces publication-title: Class. Quantum Grav. doi: 10.1088/1361-6382/aaa0a6 – volume: 59 start-page: 353 year: 2001 ident: cqgadb82abib2 article-title: The inverse mean curvature flow and the riemannian penrose inequality publication-title: J. Differ. Geom. doi: 10.4310/jdg/1090349447 – volume: 29 year: 2012 ident: cqgadb82abib7 article-title: Geometric inequalities for axially symmetric black holes publication-title: Class. Quantum Grav. doi: 10.1088/0264-9381/29/7/073001 – volume: 293 start-page: 39 year: 1992 ident: cqgadb82abib22 article-title: Lower eigenvalue estimates for dirac operators publication-title: Math. Ann. doi: 10.1007/BF01444701 – volume: 188 start-page: 121 year: 1997 ident: cqgadb82abib19 article-title: A penrose-like inequality for the mass of riemannian asymptotically flat manifolds publication-title: Commun. Math. Phys. doi: 10.1007/s002200050159 – volume: vol 77 start-page: pp 43 year: 1975 ident: cqgadb82abib18 article-title: Spectral asymmetry and riemannian geometry. I – volume: 26 year: 2009 ident: cqgadb82abib8 article-title: Present status of the penrose inequality publication-title: Class. Quantum Grav. doi: 10.1088/0264-9381/26/19/193001 – start-page: pp 39 year: 2004 ident: cqgadb82abib9 article-title: The penrose inequality – volume: 51 start-page: 1 year: 2019 ident: cqgadb82abib15 article-title: A penrose-type inequality with angular momentum and charge for axisymmetric initial data publication-title: Gen. Relativ. Gravit. doi: 10.1007/s10714-019-2600-8 – volume: 79 start-page: 33 year: 2008 ident: cqgadb82abib6 article-title: Proof of the angular momentum-mass inequality for axisymmetric black holes publication-title: J. Differ. Geome. doi: 10.4310/jdg/1207834657 – volume: 59 start-page: 177 year: 2001 ident: cqgadb82abib3 article-title: Proof of the riemannian penrose inequality using the positive mass theorem publication-title: J. Differ. Geom. doi: 10.4310/jdg/1090349428 – volume: 23 start-page: 6857 year: 2006 ident: cqgadb82abib5 article-title: A variational principle for stationary, axisymmetric solutions of einstein’s equations publication-title: Class. Quantum Grav. doi: 10.1088/0264-9381/23/23/016 – year: 2020 ident: cqgadb82abib23 article-title: A spinor approach to penrose inequality – volume: vol 102 start-page: 631 year: 1982 ident: cqgadb82abib1 article-title: Some unsolved problems in classical general relativity – year: 1984 ident: cqgadb82abib20 – volume: 206 start-page: 137 year: 1999 ident: cqgadb82abib14 article-title: Angular momentum and positive mass theorem publication-title: Commun. Math. Phys. doi: 10.1007/s002200050700 – volume: 162 start-page: 71 year: 1970 ident: cqgadb82abib11 article-title: A variational principle for rotating stars in general relativity publication-title: Astrophys. J. doi: 10.1086/150635 – volume: 80 start-page: 381 year: 1981 ident: cqgadb82abib12 article-title: A new proof of the positive energy theorem publication-title: Commun. Math. Phys. doi: 10.1007/BF01208277 – volume: 2 year: 1984 ident: cqgadb82abib21 – volume: 21 start-page: 1 year: 1982 ident: cqgadb82abib17 article-title: Quantum theory of spin-3/2 field in Einstein spaces publication-title: Int. J. Theor. Phys. doi: 10.1007/BF01880262 – volume: 4 start-page: 277 year: 1987 ident: cqgadb82abib16 article-title: Topology and stability of marginal 2-surfaces publication-title: Class. Quantum Grav. doi: 10.1088/0264-9381/4/2/011 – volume: 2 start-page: 189 year: 1985 ident: cqgadb82abib13 article-title: Witten identities for rotations, spinor boundary-value problems and new gauge conditions for asymptotic symmetries publication-title: Class. Quantum Grav. doi: 10.1088/0264-9381/2/2/012 |
| SSID | ssj0011812 |
| Score | 2.4590137 |
| Snippet | In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set... |
| SourceID | crossref iop |
| SourceType | Index Database Publisher |
| StartPage | 65022 |
| SubjectTerms | geometric inequality momentum constraint rotating black holes |
| Title | Geometric inequality for axisymmetric black holes with angular momentum |
| URI | https://iopscience.iop.org/article/10.1088/1361-6382/adb82a |
| Volume | 42 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIOP databaseName: IOP Science Platform customDbUrl: eissn: 1361-6382 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011812 issn: 0264-9381 databaseCode: IOP dateStart: 19840101 isFulltext: true titleUrlDefault: https://iopscience.iop.org/ providerName: IOP Publishing |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFA5zIuiDl6k4b-RBH3zIljS9JPgk4jaEqQ8O9iCUpElBZBdsB85f70nbDRUF8a3QQxs-Tvt9OTkXhM5okFgvMj5h1hTRKk6UZpJElqaUmhBYyRUK9-_C3sC_HQbDGrpc1sJMptWvvwWXZaPgEsIqIU60GQ8ZAbfx2spo4YE4WuUChLGr3rt_WB4hOOoqAyw-kcBL1RnlT0_4wkkr8N5PFNPZQk-LxZWZJS-tWa5byfu3vo3_XP022qykJ74qTXdQzY4baKO_7NuaNdBakRCaZLuo27WTkZu2lWDQoWXp5RyDwsXq7Tmbj6p72sX_sJuxm2EX0sUu_AmbZTxynR3y2WgPDTo3j9c9Ug1dIInHeU4MC1KmvFQmHuOWaiWt64mlg0hrAdwOZKaEEtwaX8gwUlSHikWRTK3WgdCK76P6eDK2BwiHQqUijagysGmhVEmTskRIC5pAglcETXSxgD2elr014uJMXIjYwRQ7mOISpiY6B0Tj6gPLfrU7_KPdEVr33CRfyonHjlE9f53ZE5AXuT4t3OgDz_TIdQ |
| linkProvider | IOP Publishing |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60oujBR1Wszz3owcO2u0mT7B5FbeujtQcLvcXd7AZE-sCkYP317iZpUVEQvAUy5PExyTc7O_MNwCnxIu0Eqo6pVlm2ysVCUo4DTWJClG9YyTYKtzt-q1e_7Xv9Ys5p1gszGhe__qo5zIWCcwiLgjhWo65PsXEbpyaUZI6ojVW8CEuZTont4HvozrcRLH3lSZY65oabin3Kn67yhZcWzb0_0UxjA55mD5hXl7xUJ6msRu_ftBv_8QabsF6EoOgiN9-CBT0sw1p7rt-alGE5KwyNkm1oNvVoYKduRcjEo3kL5hSZSBeJt-dkOijOSZsHRHbWboJsahfZNKhZNKOBVXhIJ4Md6DWuHy9buBi-gCPHdVOsqBdT4cQ8cqiriRRcW20s6QVSMsPxhtQEE8zVqs64HwgifUGDgMdaSo9J4e5CaTga6j1APhMxiwMilFm8ECK4imnEuDaxATfe4VXgfAZ9OM41NsJsb5yx0EIVWqjCHKoKnBlUw-JDS3612_-j3QmsdK8a4f1N5-4AVh073Je42KGHUEpfJ_rIRBypPM686gP4BM3W |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Geometric+inequality+for+axisymmetric+black+holes+with+angular+momentum&rft.jtitle=Classical+and+quantum+gravity&rft.au=Feng%2C+Xuefeng&rft.au=Yan%2C+Ruodi&rft.au=Gao%2C+Sijie&rft.au=Lau%2C+Yun-Kau&rft.date=2025-03-21&rft.issn=0264-9381&rft.eissn=1361-6382&rft.volume=42&rft.issue=6&rft.spage=65022&rft_id=info:doi/10.1088%2F1361-6382%2Fadb82a&rft.externalDBID=n%2Fa&rft.externalDocID=10_1088_1361_6382_adb82a |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0264-9381&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0264-9381&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0264-9381&client=summon |