# Holographic Entanglement Entropy on Generic Time Slices

## TL;DR

This paper investigates holographic entanglement entropy and mutual information for boosted subsystems, revealing divergences and limitations in non-relativistic theories, and highlighting differences from relativistic cases.

## Contribution

It demonstrates the divergence of mutual information at light-like separations and shows entanglement entropy issues in non-relativistic geometries, indicating restrictions on Hilbert space factorization.

## Key findings

- Mutual information diverges universally at light-like separation.
- Holographic entanglement entropy is ill-defined in non-relativistic geometries.
- Hilbert space factorization is limited to constant time slices in non-relativistic theories.

## Abstract

We study the holographic entanglement entropy and mutual information for Lorentz boosted subsystems. In holographic CFTs at zero and finite temperature, we find that the mutual information gets divergent in a universal way when the end points of two subsystems are light-like separated. In Lifshitz and hyperscaling violating geometries dual to non-relativistic theories, we show that the holographic entanglement entropy is not well-defined for Lorentz boosted subsystems in general. This strongly suggests that in non-relativistic theories, we cannot make a real space factorization of the Hilbert space on a generic time slice except the constant time slice, as opposed to relativistic field theories.