Bañados–Teitelboim–Zanelli black hole in the information geometry

Hiroaki Matsueda, Tatsuo Suzuki

Research output: Contribution to journalArticle

Abstract

We examine the Bañados–Teitelboim–Zanelli (BTZ) black hole in terms of the information geometry and consider what kind of quantum information produces the black hole metric in close connection with the anti-de Sitter space= conformal field theory (AdS=CFT) correspondence. We find a Hessian potential that exactly produces both the BTZ metric and the entanglement entropy formula for CFT1+1 at a finite temperature. Taking a free-falling frame near the event horizon is a key procedure to derive these exact results. We also find an alternative Hessian potential that produces the same BTZ metric, which is found using the duality relation based on the Legendre transformation. We realize that the dual representation originates from the entanglement Hamiltonian on the CFT side. Our results suggest that the present information-geometrical approach is very powerful for understanding the mechanism of the holographic renormalization group such as the AdS/CFT correspondence.

LanguageEnglish
Article number104001
JournalJournal of the Physical Society of Japan
Volume86
Issue number10
DOIs
StatePublished - 2017 Oct 15

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geometry
Legendre functions
event horizon
falling
entropy
temperature

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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Bañados–Teitelboim–Zanelli black hole in the information geometry. / Matsueda, Hiroaki; Suzuki, Tatsuo.

In: Journal of the Physical Society of Japan, Vol. 86, No. 10, 104001, 15.10.2017.

Research output: Contribution to journalArticle

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