Nonexistence of Marginally Trapped Surfaces and Geons in 2 + 1 Gravity

Gregory J Galloway, Kristin Schleich, Donald M. Witt

Research output: Contribution to journalArticle

Abstract

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2 + 1 gravity to obtain nonexistence of geons in 2 + 1 gravity. In particular, our results show that any 2 + 1 initial data set, which obeys the dominant energy condition with cosmological constant Λ ≥ 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2 + 1 gravity but also apply to quantum 2 + 1 gravity when formulated using Witten's solution space quantization.

Original languageEnglish (US)
Pages (from-to)285-298
Number of pages14
JournalCommunications in Mathematical Physics
Volume310
Issue number2
DOIs
StatePublished - Mar 2012

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Nonexistence
Gravity
gravitation
convexity
Null
Convexity
Cosmological Constant
Existence Results
Quantization
Trivial
cut-off
topology
boundary conditions
Topology
Boundary conditions
Energy
energy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Nonexistence of Marginally Trapped Surfaces and Geons in 2 + 1 Gravity. / Galloway, Gregory J; Schleich, Kristin; Witt, Donald M.

In: Communications in Mathematical Physics, Vol. 310, No. 2, 03.2012, p. 285-298.

Research output: Contribution to journalArticle

Galloway, Gregory J ; Schleich, Kristin ; Witt, Donald M. / Nonexistence of Marginally Trapped Surfaces and Geons in 2 + 1 Gravity. In: Communications in Mathematical Physics. 2012 ; Vol. 310, No. 2. pp. 285-298.
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