# Gravitation in flat spacetime from entanglement

## TL;DR

This paper investigates holographic entanglement entropy in Minkowski spacetime, refining computational methods and establishing a link between the first law of entanglement and gravitational equations of motion in flat spacetime.

## Contribution

It refines the holographic entanglement entropy prescription for Minkowski space and connects entanglement laws to gravitational dynamics in flat spacetime.

## Key findings

- Refined the Ryu-Takayanagi formula for 3D Minkowski space.
- Proposed a generalization of the entanglement entropy prescription to 4D.
- Showed the first law of entanglement implies linearized Einstein equations in flat spacetime.

## Abstract

We explore holographic entanglement entropy for Minkowski spacetime in three and four dimensions. Under some general assumptions on the putative holographic dual, the entanglement entropy associated to a special class of subregions can be computed using an analog of the Ryu-Takayanagi formula. We refine the existing prescription in three dimensions and propose a generalization to four dimensions. Under reasonable assumptions on the holographic stress tensor, we show that the first law of entanglement is equivalent to the gravitational equations of motion in the bulk, linearized around Minkowski spacetime.