Holographic entanglement entropy of the BTZ black hole

TL;DR

This paper derives explicit formulas for the holographic entanglement entropy of the BTZ black hole in 3D AdS gravity, showing it reproduces the Bekenstein-Hawking entropy and relates to 2D CFT partition functions, highlighting the emergent nature of black hole entropy.

Contribution

It provides explicit formulas for holographic EE of the BTZ black hole and links it to 2D CFT partition functions, emphasizing the emergent aspect of black hole entropy.

Findings

Holographic EE reproduces Bekenstein-Hawking entropy at leading order.

Subleading term in EE behaves as ln S_BH.

Black hole EE emerges from semiclassical spacetime geometry.

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 AdS$_{3}$. 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.