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Uniqueness of the asymptotic AdS3 geometry

M Rooman1,3 and Ph Spindel2

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We show explicitly that in (2 + 1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neighbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.


PACS

04.20.Ex Initial value problem, existence and uniqueness of solutions

04.20.Ha Asymptotic structure

04.70.-s Physics of black holes

02.40.-k Geometry, differential geometry, and topology

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)

83C57 Black holes

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 11 (7 June 2001)

Received 5 February 2001



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