Holographic entanglement entropy for black strings

Abstract

The holographic entanglement entropy (HEE) of field theories dual to 4-dimensional black strings with both the infinity boundary and near the horizon is investigated. It is shown that, with the infinity boundary, the main contribution of the HEE is divergent and it comes from the AdS background. If we remove this contribution, the remaining part is finite and proportional to the mass and charge densities. Near the horizon, we find that the HEE equals the Bekenstein–Hawking entropy if the subsystem covers the whole conformal boundary, for both charged and uncharged cases. In particular, the minimal surface (Ryu–Takayanagi surface) always stays in the bulk region for uncharged and non-extremal charged cases, while it is immersed inside the boundary for extremal black string.