Banados-Teitelboim-Zanelli Black Hole in the Information Geometry

Understand

We examine the Banados-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.