Planar Black holes and Entanglement Entropy in Analog Gravity Models

TL;DR

This work advances analogue gravity by constructing a relativistic fluid model whose perturbations reproduce scalar-field dynamics in space-times conformal to static planar black holes. It shows how a conformal factor and a blackening function can be incorporated to realize a broad class of planar BH geometries and how the perturbation mass can be tuned via the external potential, enabling flexible simulations of horizon-related phenomena. The authors introduce and compute analog holographic entanglement entropy for planar AdS5 black holes, using minimal-surface prescriptions and strip geometries, demonstrating area-law behavior in the appropriate limit. Collectively, the results significantly broaden the set of explicitly known analogue metrics, strengthen links to gauge/gravity duality, and pave the way for laboratory tests of gravity-inspired entanglement structures in condensed-matter platforms.

Abstract

Via constructing an explicit Lagrangian for which the perturbation equations are analogues of a scalar field propagating in a planar black hole space-time, it is found that all planar black holes conformal to a Painlevé--Gullstrand type line element can be realized as analogue metrics. We also introduce the concept of holographic entanglement entropy for planar black-hole space-times. This is valid for an arbitrary choice of conformal and blackening factor, thereby vastly extending the number of known examples of explicitly known analogue metrics.

Figures (2)

• Figure 1: Strip geometry employed to calculate the entanglement entropy.
• Figure 2: Holographic entanglement entropy (full black line) and limiting function $S_{\rm lim}$ (blue dashed line) versus strip width.