# The Holographic Entropy Cone in AdS-Vaidya Spacetimes

## TL;DR

This paper investigates the validity of holographic entropy cone inequalities in dynamical AdS-Vaidya spacetimes, demonstrating they hold under null energy conditions and providing numerical evidence for their general applicability.

## Contribution

It provides numerical analysis of five-region holographic entropy inequalities in dynamical spacetimes, supporting their validity beyond static cases.

## Key findings

- Inequalities hold when null energy condition is satisfied.
- Inequalities are violated when null energy condition is violated.
- Numerical solutions support the conjecture that inequalities hold in dynamical spacetimes.

## Abstract

We examine the five-region holographic entropy cone inequalities for the special case of the AdS$_3$-Vaidya metric for a variety of boundary configurations. This is done by numerically solving the geodesic equation in the bulk for various boundary configurations. In all the cases we examine, we find that all the inequalities are satisfied when the bulk satisfies the null energy condition, while the inequalities are all violated when the bulk spacetime violates the null energy condition. A proof of the five-region holographic entropy cone inequalities for the dynamical bulk case remains an open problem--our results provide evidence that these inequalities hold for dynamical bulk spacetimes.