Skip to main content
SpringerLink
Log in

Black Holes and Wormholes in 2+1 Dimensions

  • Conference paper
  • First Online:
Mathematical and Quantum Aspects of Relativity and Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 537))

Abstract

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally “anti-de Sitter” spaces is treated in an elementary way, using visualizable models. Among the objects discussed are black holes, spaces with multiple black holes, their horizon structure, closed universes, and the topologies that are possible.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bañados, M., Teitelboim, C., Zanelli, J., (1992) The black hole in three-dimensional space-time. Phys. Rev. Lett. 69, 1849–1851; Bañados, M., Henneaux, M., Teitelboim, C., Zanelli, J. (1993) Geometry of the (2+1) black hole. Phys. Rev. D48, 1506-1525

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Mess, G. (1990) Lorentz spacetimes of constant curvature. IHES preprint

    Google Scholar 

  3. Morrow-Jones, J., Witt, D. (1993) Inflationary initial data for generic spatial topology. Phys. Rev. D 48, 2516–2528

    ADS  MathSciNet  Google Scholar 

  4. Misner, C. (1967) Taub-NUT space as a counterexample to almost anything. In Relativity Theory and Astrophysics I, ed. J. Ehlers, Lectures in Applied Mathematics 8, 160–169

    Google Scholar 

  5. Benedetti R., Petronio, C. (1992) Lectures on Hyperbolic Geometry. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  6. Carlip, S (1998) Quantum gravity in 2+1 dimensions. Cambridge University Press

    Google Scholar 

  7. Holst, S. (1996) Gott time machines in anti-de Sitter space. Gen. Rel. Grav. 28, 387–403; Åminneborg, S., Bengtsson, I., Holst, D., Peldán, P. (1996) Making anti-de Sitter black holes. Class. Quant. Grav. 13, 2707-2714

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Li, Li-Xin (1999) Time machines constructed from anti-de Sitter space. Phys. Rev. D59, 084016

    Google Scholar 

  9. Bachmann F. (1973) Aufbau der Geometrie aus dem Spiegelungsbegriff. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  10. Flamm, L (1916) Beiträge zur Einsteinschen Gravitationstheorie. Phys. Z. 17, 448–454, or see Misner, C., Thorne, K., Wheeler, J., (1973) Gravitation (p. 614). Freeman, San Francisco; Marolf, D. (1999) Space-time embedding diagrams for black holes. Gen. Rel. Grav. 31, 919-944

    Google Scholar 

  11. Brill, D. (1996) Multi-black hole geometries in (2+1)-dimensional gravity. Phys. Rev. D 53, 4133-4176; Steif, A. (1996) Time-Symmetric initial data for multibody solutions in three dimensions. Phys. Rev. D 53, 5527-5532

    Google Scholar 

  12. Susskind, L. (1995) The world as a hologram. J. Math. Phys. 36, 6377–6396; Witten, E. (1998) Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253-291

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Holst, S. (1997) On black hole safari in anti-de Sitter space. Filosofie Licentiaexamen, Dept. of Phys., Stockholm Univ.

    Google Scholar 

  14. Åminneborg, S., Bengtsson, I., Brill, D., Holst, D., Peldán, P. (1998) Black holes and wormholes in 2+1 dimensions. Class. Quant. Grav. 15, 627–644

    Article  MATH  ADS  Google Scholar 

  15. Åminneborg, S., Bengtsson, I., Holst, S (1999) A spinning anti-de Sitter wormhole. Class. Quant. Grav. 16, 363–382

    Article  MATH  ADS  Google Scholar 

  16. Holst, S., Peldán, P. (1997) Black holes and causal structure in anti-de Sitter isomorphic spacetimes. Class. Quant. Grav. 14, 3433–3452

    Article  MATH  ADS  Google Scholar 

  17. Carlip, S., Gegenberg, J., Mann, R., (1995) Black holes in three-dimensional topological gravity. Phys. Rev. D 51, 6854–6859; Abbott, L., Deser, S. (1982) Stability of gravity with a cosmological constant. Nucl. Phys. B 195, 76; Brown, J., Creighton, J., Mann, R. (1994) Temperature, energy and heat capacity of asymptotically anti-de Sitter black holes. Phys. Rev. D 50, 6394-6403

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Maryland, 20742, College Park, MD, USA

    Dieter Brill

  2. Albert-Einstein-Institut, Potsdam, FRG, Germany

    Dieter Brill

Authors
  1. Dieter Brill
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Laboratory for Geometry, Dynamical System and Cosmology Department of Mathematics, University of the Aegean, 83 200, Karlovassi, Greece

    Spiros Cotsakis

  2. DAMTP, University of Cambridge, Silver Street, CB3 9EW, Cambridge, UK

    Gary W. Gibbons

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brill, D. (2000). Black Holes and Wormholes in 2+1 Dimensions. In: Cotsakis, S., Gibbons, G.W. (eds) Mathematical and Quantum Aspects of Relativity and Cosmology. Lecture Notes in Physics, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46671-1_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-46671-1_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66865-7

  • Online ISBN: 978-3-540-46671-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation