Generalized Rindler Wedge and Holographic Observer Concordance

TL;DR

This paper introduces a new way to define gravitational subsystems using accelerating observers and their horizons, establishing a holographic framework that links observer-based partitions to holographic dualities and entanglement entropy.

Contribution

It defines generalized Rindler wedges based on spacelike surfaces satisfying a global convexity condition, linking observer horizons to holographic duality and entanglement entropy.

Findings

Entanglement entropy proportional to the surface area of Rindler-convex regions

Holographic interpretation of generalized Rindler wedges supported by multiple evidence

Establishment of a holographic observer concordance framework

Abstract

Defining gravitational subsystems has long been challenging due to the lack of the conventional notion of locality in gravity. In this work, we define gravitational subsystems from the observable spacetime subregions of a set of well-defined accelerating observers. We study the most general horizons of accelerating observers and find that in a general spacetime, only spacelike surfaces satisfying a global condition could become horizons of well-defined accelerating observers, which we name the Rindler-convexity condition. The entanglement entropy associated with a Rindler-convex region is proportional to the area of the enclosing surface. The subregions defined from this observer perspective is named the generalized Rindler wedge. This provides a physical origin for defining gravitational subsystems associated with one type of Type III von Neumann subalgebra. We propose the holographic interpretation of generalized Rindler wedges and provide evidence from the observer correspondence, the subregion subalgebra duality, and the equality of the entanglement entropy, respectively. We introduce time/space cutoffs in the bulk to substantiate this proposition, generalize it, and establish a holographic observer concordance framework, which asserts that the partitioning of degrees of freedom through observation is holographically concordant.