Holographic Entanglement Entropy of the BTZ Black Hole

2009/07/22 by Mariano Cadoni, M. Cadoni, Maurizio Melis +1 · 1 citation
Physics and Astronomy · #BTZ black hole #Black Holes and Theoretical Physics #Black brane #Black hole thermodynamics #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Extremal black hole #Holography #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Theoretical physics #hep-th

paper · pdf · doi:10.1007/s10701-010-9430-6

published as Found.Phys.40:638-657,2010 · We added the comparison of some of our results with previous results for the quantum entropy of a scalar in the Euclidean BTZ background. Two more references have been also added

arxiv created 2009/07/22 · openalex publication_date 2010/02/11 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S_BH, whereas the subleading term behaves as ln S_BH. We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.

Citations

• Black hole in three-dimensional spacetime
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Thermodynamics of black holes in anti-de Sitter space
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• Black hole thermodynamics and information loss in two dimensions
• Entanglement Entropy of Black Holes and Anti–de Sitter Space/Conformal-Field-Theory Correspondence
• Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Symmetries, horizons, and black hole entropy
• Geometry of the 2+1 Black Hole

Cited by

• Logarithmic corrections to the entropy of scalar field in BTZ black hole spacetime