Entanglement surfaces for rotating cylindrical black holes

Abstract

We construct entanglement surfaces for rotating cylindrical black holes in a double holographic setup, extending previous results to the case of stationary backgrounds. We analyze both the 5d braneworld construction as well as the embedding in 10d type IIB string theory. We couple the rotating cylindrical black hole to a non-gravitating bath, and study island and Hartman-Maldacena surfaces. Properties of island surfaces are characterized by three regimes, bounded by two critical parameters. In addition to the critical value known for the static case, we find that a new one emerges, related to the extremal limit of the rotating black hole. This behaviour is present both for the bottom-up as well as the top-down models, for which we find qualitative agreement.

Figures (14)

• Figure 1.1: Penrose diagram of the rotating cylindrical black hole at finite temperature (left) and at extremality (right).
• Figure 2.2: Sketch of the black string geometry \ref{['eq:5DBlackStringGeometry']}, with the two classes of bulk extremal surfaces homologous to a given bath subregion $\mathcal{R}$. Each $\mu=const.$ slice hosts the cylindrical black hole \ref{['eq:RotatingCylindricalBH']}. Island surfaces end on the brane, while HM surfaces end on the horizon.
• Figure 2.3: Behavior of the island surfaces in the static black brane geometry, below (left) and above (right) the critical angle $\mu_c$. Below the critical angle, the region on the brane where islands can end, i.e. the atoll, depicted in green, does not cover the whole brane.
• Figure 2.4: Behavior of island surfaces in the three regimes I, $\mu_0>\mu_c$, at the top, II, for $\mu_e<\mu_0<\mu_c$, middle row, and III, $\mu_0<\mu_e$, bottom row. Curves with the same color are associated with the same value of $\Omega$, which increases ($r_h$ decreases) from the static solution (blue curve $\Omega=0,$$r_h=0$), to the near extremal case (red curve $1-\Omega=5\cdot10^{-6},$$r_h=-4$). Black lines correspond to the extremal solution.
• Figure 2.5: Behavior of island surfaces in the extremal limit at fixed $r_R$ in regimes (I,II), here with $\mu_0 = 0.9>\mu_e$ (left), and III with $\mu_0=0.35<\mu_e$ (right). We show the radial coordinate $e^r$ so taht the horizon is located at $e^r=0$ at extremality. The black dashed curve corresponds to the HM surface at $r_h=-15$, very close to extremality. In regime III this curve essentially coincide with the corresponding island surface (solid black).