World Library  
Flag as Inappropriate
Email this Article

BTZ black hole

Article Id: WHEBN0017143970
Reproduction Date:

Title: BTZ black hole  
Author: World Heritage Encyclopedia
Language: English
Subject: Cardy formula, Time travel, MTZ black hole, Black holes, Quantum gravity
Collection: Black Holes, Mathematical Methods in General Relativity, Quantum Gravity
Publisher: World Heritage Encyclopedia

BTZ black hole

The BTZ black hole, named after black hole solution for (2+1)-dimensional gravity with a negative cosmological constant.


  • History 1
  • Properties 2
  • The case without charge 3
  • See also 4
  • References 5


In 1992 Bañados, Teitelboim and Zanelli discovered BTZ black hole(Bañados, Teitelboim & Zanelli 1992). At that time, it came as a surprise because it is believed that no black hole solutions are shown to exist for a negative cosmological constant and BTZ black hole has remarkably similar properties to the 3+1 dimensional black hole, which would exist in our real universe.

When the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat, and it can be shown that no black hole solutions with event horizons exist. By introducing dilatons, we can have black holes. We do have conical angle deficit solutions, but they don't have event horizons. It therefore came as a surprise when black hole solutions were shown to exist for a negative cosmological constant.


The similarities to the ordinary black holes in 3+1 dimensions:

  • It has "no hairs" (No hair theorem) and is fully characterized by ADM-mass, angular momentum and charge.
  • It has the same thermodynamical properties as the ordinary black holes, e.g. its entropy is captured by a law directly analogous to the Bekenstein bound in (3+1)-dimensions, essentially with the surface area replaced by the BTZ black hole's circumference.
  • Like the Kerr black hole, a rotating BTZ black hole contains an inner and an outer horizon. see also Ergosphere.

Since (2+1)-dimensional gravity has no Newtonian limit, one might fear that the BTZ black hole is not the final state of a gravitational collapse. It was however shown, that this black hole could arise from collapsing matter and we can calculate the energy-moment tensor of BTZ as same as (3+1) black holes. (Carlip 1995) section 3 Black Holes and Gravitational Collapse.

The BTZ solution is often discussed in the realm on (2+1)-dimensional quantum gravity.

The case without charge

The metric in the absence of charge is

ds^2 = -\frac{(r^2 - r_+^2)(r^2 - r_-^2)}{l^2 r^2}dt^2 + \frac{l^2 r^2 dr^2}{(r^2 - r_+^2)(r^2 - r_-^2)} + r^2 \left(d\phi - \frac{r_+ r_-}{l r^2} dt \right)^2

where r_+,~r_- are the black hole radii and l is the radius of AdS3 space. The mass and angular momentum of the black hole is

M = \frac{r_+^2 + r_-^2}{l^2},~~~~~J = \frac{2r_+ r_-}{l}

BTZ black holes without any electric charge are locally isometric to anti-de Sitter space. More precisely, it corresponds to an orbifold of the universal covering space of AdS3.

A rotating BTZ black hole admits closed timelike curves.

See also


  • Bañados, Máximo; Teitelboim, Claudio; Zanelli, Jorge (1992), The Black hole in three-dimensional space-time, Phys.Rev.Lett. 69,  url=
  • Carlip, Steven (2005), Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole, arxiv url=
  • Carlip, Steven (1995), The (2+1)-Dimensional Black Hole, arxiv url=
  • Bañados, Máximo (1999), Three-dimensional quantum geometry and black holes, arxiv url=
  • Daisuke, Ida (2000), No Black Hole Theorem in Three-Dimensional Gravity, Phys. Rev. Lett. 85 3758  url=
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.