### 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 CFT_{1+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.

Language | English |
---|---|

Article number | 104001 |

Journal | Journal of the Physical Society of Japan |

Volume | 86 |

Issue number | 10 |

DOIs | |

State | Published - 2017 Oct 15 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*86*(10), [104001]. DOI: 10.7566/JPSJ.86.104001

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

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 86, no. 10, 104001. DOI: 10.7566/JPSJ.86.104001

}

TY - JOUR

T1 - Bañados–Teitelboim–Zanelli black hole in the information geometry

AU - Matsueda,Hiroaki

AU - Suzuki,Tatsuo

PY - 2017/10/15

Y1 - 2017/10/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85031002727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031002727&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.86.104001

DO - 10.7566/JPSJ.86.104001

M3 - Article

VL - 86

JO - Journal of the Physical Society of Japan

T2 - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

M1 - 104001

ER -