Skip to main content
SpringerLink
Log in

How Unique Are Higher-dimensional Black Holes?

  • Chapter
  • First Online:
Quantum Field Theory and Gravity

  • 2187 Accesses

Abstract

In this article, we review the classification and uniqueness of stationary black hole solutions having large abelian isometry groups in higher-dimensional general relativity. We also point out some consequences of our analysis concerning the possible topologies that the black hole exteriors may have.

Mathematics Subject Classification (2010). 35Q75, 53C43, 58D19.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. Amsel, A. J., Horowitz, G. T., Marolf, D. and Roberts, M. M.: arXiv:0906.2367 [gr-qc]

    Google Scholar 

  2. Bunting, G. L.: PhD Thesis, Univ. of New England, Armidale, N.S.W., 1983

    Google Scholar 

  3. Carter, B.: Phys. Rev. Lett. 26, 331-333 (1971)

    Article  Google Scholar 

  4. Chruściel, P. T.: Commun. Math. Phys. 189, 1-7 (1997)

    Google Scholar 

  5. Chruściel, P. T. and Lopes Costa, J.: arXiv:0806.0016 [gr-qc]

    Google Scholar 

  6. Chruściel, P. T.: J. Math. Phys. 50, 052501 (2009)

    Google Scholar 

  7. Chruściel, P. T., Galloway, G. J. and Solis, D.: Annales Henri Poincaré 10, 893 (2009)

    Google Scholar 

  8. Emparan, R., Harmark, T., Niarchos V. and Obers, N. A.: arXiv:1106.4428 [hep-th] and references therein

    Google Scholar 

  9. Emparan, R. and Reall, H. S.: Living Rev. Rel. 11, 6 (2008)

    Google Scholar 

  10. Figueras, P. and Lucietti, J.: arXiv:0906.5565 [hep-th]

    Google Scholar 

  11. Friedrich, H., Rácz, I. and Wald, R. M.: Commun. Math. Phys. 204, 691-707 (1999)

    Google Scholar 

  12. Galloway, G. J., Schleich, K., Witt, D. M. and Woolgar, E.: Phys. Rev. D 60, 104039 (1999)

    Article  MathSciNet  Google Scholar 

  13. Galloway, G. J. and Schoen, R: Commun. Math. Phys. 266, 571576 (2006)

    MathSciNet  Google Scholar 

  14. Gibbons, G. W., Ida, D. and Shiromizu, T.: Phys. Rev. Lett. 89, 041101 (2002), arXiv:hep-th/0206049

    Google Scholar 

  15. Harmark, T.: Phys. Rev. D 70, 124002 (2004)

    Article  MathSciNet  Google Scholar 

  16. Hawking, S. W. and Ellis, G. F. R.: Cambridge, Cambridge University Press, 1973

    Google Scholar 

  17. Hawking, S. W.: Commun. Math. Phys. 25, 152-166 (1972)

    Article  MathSciNet  Google Scholar 

  18. Hollands, S., Ishibashi, A. and Wald, R. M.: Commun. Math. Phys. 271, 699 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hollands, S. and Ishibashi, A.: Commun. Math. Phys. 291, 403 (2009)

    Article  MathSciNet  Google Scholar 

  20. Hollands, S. and Ishibashi, A.: arXiv:0909.3462 [gr-qc]

    Google Scholar 

  21. Hollands, S., Holland, J. and Ishibashi, A.: arXiv:1002.0490 [gr-qc]

    Google Scholar 

  22. Hollands, S. and Yazadjiev, S.: Commun. Math. Phys. 283, 749 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hollands, S. and Yazadjiev, S.: arXiv:0812.3036 [gr-qc].

    Google Scholar 

  24. Israel, W.: Phys. Rev. 164, 1776-1779 (1967)

    Article  Google Scholar 

  25. Kunduri, H. K., Lucietti, J. and Reall, H. S.: Class. Quant. Grav. 24, 4169 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kunduri, H. K. and Lucietti, J.: J. Math. Phys. 50, 082502 (2009)

    Article  MathSciNet  Google Scholar 

  27. Maison, D.: Gen. Rel. Grav. 10, 717 (1979)

    Article  MathSciNet  Google Scholar 

  28. Mazur, P. O.: J. Phys. A 15, 3173-3180 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  29. Melvin, P.: Math. Proc. Camb. Phil. Soc. 91, 305-314 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  30. Moncrief, V. and Isenberg, J.: Commun. Math. Phys. 89, 387-413 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  31. Moncrief, V. and Isenberg, J.: Class. Quant. Grav. 25, 195015 (2008)

    Article  MathSciNet  Google Scholar 

  32. Morisawa, Y. and Ida, D.: Phys. Rev. D 69, 124005 (2004)

    Article  MathSciNet  Google Scholar 

  33. Oh, H. S.: Topology Appl. 13, 137-154 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  34. Orlik, P. and Raymond, F.: Topology 13, 89-112 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  35. Rácz, I.: Class. Quant. Grav. 17, 153 (2000)

    Google Scholar 

  36. Robinson, D. C.: Phys. Rev. Lett. 34, 905-906 (1975)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

    Stefan Hollands

Authors
  1. Stefan Hollands
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Hollands .

Editor information

Editors and Affiliations

  1. , Lehrstuhl für Mathematik, Universität Regensburg, Universitätsstr. 31, Regensburg, 93053, Germany

    Felix Finster

  2. , Lehrstuhl für Mathematik, Universität Regensburg, Universitätsstr. 31, Regensburg, 93053, Germany

    Olaf Müller

  3. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Marc Nardmann

  4. in den Naturwissenschaften, Max-Planck-Institut für Mathematik, Inselstr. 22-26, Leipzig, 04103, Germany

    Jürgen Tolksdorf

  5. in den Naturwissenschaften, Max-Planck-Institut für Mathematik, Inselstr. 22-26, Leipzig, 04103, Germany

    Eberhard Zeidler

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Basel AG

About this chapter

Cite this chapter

Hollands, S. (2012). How Unique Are Higher-dimensional Black Holes?. In: Finster, F., Müller, O., Nardmann, M., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory and Gravity. Springer, Basel. https://doi.org/10.1007/978-3-0348-0043-3_15

Download citation

Publish with us

Policies and ethics

Search

Navigation