Observer dependence in holographic entanglement entropy

Abstract

The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence conjectures a duality between gravitational theories in asymptotically Anti-de Sitter (AdS) spacetimes and non-gravitational quantum conformal field theories (CFTs) defined on the boundary of the gravitational spacetimes. This correspondence provides strong evidence for the holographic nature of gravity while also giving insight into the relationship between gravity and quantum mechanics. These ideas have been sharpened by the holographic entanglement entropy results of Ryu, Takayanagi, Rangamani, and Hubeny. However, most holographic entanglement entropy results are restricted to the technically simple setting of (2 + 1)-dimensional gravity. These have suggested a distinct relationship between thermal entropy of black holes in the gravitational theory and entanglement entropy corresponding to thermal states in the CFT. In higher dimensions, there exist black holes whose event horizon area (and seemingly thermal properties) are highly observer dependent. We find that, although this observer dependence does not carry over to the holographic entanglement entropy, there is an indication of a coordinate system which is best adapted for the holographic calculation. These coordinates only cover two regions of the spacetime which exactly correspond to the regions of the CFT on which particle modes are well defined and so we see that the holographic calculation in the spacetime is capable of predicting parts of the CFT where particles cannot exist.