Rigidity of outermost MOTS: the initial data version

Research output: Contribution to journalArticle

Abstract

In the paper Commun Anal Geom 16(1):217–229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the “borderline case” in the author’s work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571–576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.

Original languageEnglish (US)
Article number32
JournalGeneral Relativity and Gravitation
Volume50
Issue number3
DOIs
StatePublished - Mar 1 2018

Fingerprint

rigidity
topology
curvature
scalars

Keywords

  • Black hole topology
  • Marginally outer trapped surfaces
  • Rigidity

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Rigidity of outermost MOTS : the initial data version. / Galloway, Gregory J.

In: General Relativity and Gravitation, Vol. 50, No. 3, 32, 01.03.2018.

Research output: Contribution to journalArticle

@article{c0fda247ee0447b09f4d7d21dd72a34b,
title = "Rigidity of outermost MOTS: the initial data version",
abstract = "In the paper Commun Anal Geom 16(1):217–229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the “borderline case” in the author’s work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571–576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.",
keywords = "Black hole topology, Marginally outer trapped surfaces, Rigidity",
author = "Galloway, {Gregory J}",
year = "2018",
month = "3",
day = "1",
doi = "10.1007/s10714-018-2353-9",
language = "English (US)",
volume = "50",
journal = "General Relativity and Gravitation",
issn = "0001-7701",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Rigidity of outermost MOTS

T2 - the initial data version

AU - Galloway, Gregory J

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In the paper Commun Anal Geom 16(1):217–229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the “borderline case” in the author’s work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571–576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.

AB - In the paper Commun Anal Geom 16(1):217–229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the “borderline case” in the author’s work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571–576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.

KW - Black hole topology

KW - Marginally outer trapped surfaces

KW - Rigidity

UR - http://www.scopus.com/inward/record.url?scp=85042561368&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042561368&partnerID=8YFLogxK

U2 - 10.1007/s10714-018-2353-9

DO - 10.1007/s10714-018-2353-9

M3 - Article

AN - SCOPUS:85042561368

VL - 50

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 3

M1 - 32

ER -