Annales Henri Poincaré

, Volume 10, Issue 7, pp 1359–1376 | Cite as

Formation of Higher-dimensional Topological Black Holes

  • Filipe C. MenaEmail author
  • José Natário
  • Paul Tod


We study higher-dimensional gravitational collapse to topological black holes in two steps. First, we construct some (n + 2)-dimensional collapsing space–times, which include generalised Lemaître–Tolman–Bondi-like solutions, and we prove that these can be matched to static Λ-vacuum exterior space–times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Second, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizoń–Chmaj–Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution.


Black Hole Event Horizon Einstein Equation Fundamental Form Gravitational Collapse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akbar M.M.: Classical boundary-value problem in Riemannian quantum gravity and Taub–Bolt-anti-de Sitter geometries. Nucl. Phys. B 663, 215–230 (2003)zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Birmingham D.: Topological black holes in anti-de Sitter space. Class. Quantum Grav. 16, 1197–1205 (1999)zbMATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Bizoń P., Chmaj T., Schmidt B.G.: Critical behaviour in vacuum gravitational collapse in 4 + 1-dimensions. Phys. Rev. Lett. 95, 071102 (2005)CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Bizoń P., Chmaj T., Rostworowski A., Schmidt B.G., Tabor Z.: Vacuum gravitational collapse in nine dimensions. Phys. Rev. D 72, 121502 (2005)CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Böhm C.: Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces. Invent. Math. 134, 145 (1998)zbMATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Boutaleb-Joutei H.: The general Taub-NUT de Sitter metric as a self-dual Yang-Mills solution of gravity. Phys. Lett. B 90, 181–184 (1980)CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Dafermos M., Holzegel G.: On the nonlinear stability of higher dimensional triaxial Bianchi-IX black holes. Adv. Theor. Math. Phys. 10, 503–523 (2006)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Eguchi T., Hanson A.J.: Asymptotically flat self-dual solutions to Euclidean gravity. Phys. Lett. B 74, 249–251 (1978)CrossRefADSGoogle Scholar
  9. 9.
    Galloway G.J.: A ‘finite infinity’ version of topological censorship. Class. Quantum Grav. 13, 1471–1478 (1996)zbMATHCrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Ghosh S.G., Beesham A.: Higher dimensional inhomogeneous dust collapse and cosmic censorship. Phys. Rev. D 64, 124005 (2001)CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Gibbons G.W., Hartnoll S.A.: Gravitational instability in higher dimensions. Phys. Rev. D 66, 064024 (2002)CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Gibbons G.W., Ida D., Shiromizu T.: Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions. Prog. Theor. Phys. Suppl. 148, 284–290 (2003)CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Goswami R., Joshi P.: Cosmic censorship in higher dimensions. Phys. Rev. D 69, sss104002 (2004)MathSciNetADSGoogle Scholar
  14. 14.
    Hellaby C.: A Kruskal-like model with finite density. Class. Quantum Grav. 4, 635–650 (1987)zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Holzegel, G.: Stability and decay-rates for the five-dimensional Schwarzschild metric under biaxial perturbations. Preprint, arXiv:0808.3246 (2008)Google Scholar
  16. 16.
    Lemos J.P.S.: Gravitational collapse to toroidal, cylindrical and planar black holes. Phys. Rev. D 57, 4600–4605 (1998)CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Mena F.C., Natário J., Tod P.: Gravitational collapse to toroidal and higher genus asymptotically AdS black holes. Adv. Theor. Math. Phys. 12, 1163–1181 (2008)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Pederson H.: Eguchi–Hanson metrics with a cosmological constant. Class. Quantum Grav. 2, 579–587 (1985)CrossRefADSGoogle Scholar
  19. 19.
    Smith W.L., Mann R.B.: Formation of topological black holes from gravitational collapse. Phys. Rev. D 56, 4942–4947 (1997)CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Birkhäuser Verlag AG, Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade do MinhoBragaPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal
  3. 3.Mathematical Institute, University of OxfordOxfordUK

Personalised recommendations