AdS/CFT Duals of Topological Black Holes and the Entropy of Zero-Energy States

TL;DR

This paper explores hyperbolic black holes in AdS space within the AdS/CFT framework, revealing new features in entropy and stress tensor behavior, including unexpected entropy increases at zero energy and the dual description as Rindler states.

Contribution

It introduces the study of hyperbolic black holes in AdS/CFT, highlighting their unique entropy and stress tensor properties and their dual description as Rindler states.

Findings

Hyperbolic black holes show increased entropy without energy increase.

A zero-temperature, zero-energy density state is highly degenerate.

Entanglement entropy across Rindler horizons exceeds expectations.

Abstract

The horizon of a static black hole in Anti-deSitter space can be spherical, planar, or hyperbolic. The microscopic dynamics of the first two classes of black holes have been extensively discussed recently within the context of the AdS/CFT correspondence. We argue that hyperbolic black holes introduce new and fruitful features in this respect, allowing for more detailed comparisons between the weak and strong coupling regimes. In particular, by focussing on the stress tensor and entropy of some particular states, we identify unexpected increases in the entropy of Super-Yang-Mills theory at strong coupling that are not accompanied by increases in the energy. We describe a highly degenerate state at zero temperature and zero energy density. We also find that the entanglement entropy across a Rindler horizon in exact AdS_5 is larger than might have been expected from the dual SYM theory. Besides, we show that hyperbolic black holes can be described as thermal Rindler states of the dual conformal field theory in flat space.