General Relativity and Gravitation

, Volume 45, Issue 2, pp 427–448 | Cite as

Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

Research Article


We review the relation between AdS spacetime in 1 \(+\) 2 dimensions and the BTZ black hole (BTZbh). Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZbh. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZbh. In order to make this we use the correspondence introduced in algebraic holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism.


BTZ black hole Holography AdS spacetime AdS/CFT 



I thank my supervisor, Dr. Bernard S. Kay, for suggesting me to study equilibrium thermal states in AdS spacetime and their relation to equilibrium thermal states in the BTZbh. I also thank him for his guidance and helpful advise during this work. This work was carried out with the sponsorship of CONACYT-Mexico through the grant 302006 and a postdoctoral fellowship.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsThe University of YorkYorkUK
  2. 2.Department of PhysicsUniversity of GuanajuatoLeonMexico
  3. 3.Centro Universitario UAEM Valle de TeotihuacanAxapuscoMexico

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