Geometry of the 2+1 black hole

Máximo Bañados, Marc Henneaux, Claudio Teitelboim, and Jorge Zanelli
Phys. Rev. D 48, 1506 – Published 15 August 1993; Erratum Phys. Rev. D 88, 069902 (2013)
PDFExport Citation

Abstract

The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti–de Sitter space by a discrete subgroup of SO(2,2). The generic black hole is a smooth manifold in the metric sense. The surface r=0 is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at r=0 to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti–de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum. A thorough classification of the elements of the Lie algebra of SO(2,2) is given in an appendix.

  • Received 11 January 1993

DOI:https://doi.org/10.1103/PhysRevD.48.1506

©1993 American Physical Society

Erratum

Erratum: Geometry of the 2+1 black hole [Phys. Rev. D 48, 1506 (1993)]

Máximo Bañados, Marc Henneaux, Claudio Teitelboim, and Jorge Zanelli
Phys. Rev. D 88, 069902 (2013)

Authors & Affiliations

Máximo Bañados

  • Centro de Estudios Científicos de Santiago, Casilla 16443, Santiago 9, Chile
  • Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

Marc Henneaux

  • Centro de Estudios Científicos de Santiago, Casilla 16443, Santiago 9, Chile
  • Faculté des Sciences, Université Libre de Bruxelles, Campus Plaine, CP231, B-1050, Bruxelles, Belgium

Claudio Teitelboim

  • Centro de Estudios Científicos de Santiago, Casilla 16443, Santiago 9, Chile, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
  • Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540

Jorge Zanelli

  • Centro de Estudios Científicos de Santiago, Casilla 16443, Santiago 9, Chile
  • Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

References (Subscription Required)

Click to Expand
Issue

Vol. 48, Iss. 4 — 15 August 1993

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×