# Entanglement entropy of linearized gravitons in a sphere

## TL;DR

This paper calculates the entanglement entropy of linearized gravitons in a spherical region in flat space, revealing a universal logarithmic coefficient consistent with mutual information results.

## Contribution

It introduces a gauge fixing and mode decomposition that simplifies the graviton entanglement entropy to that of free scalars, providing a novel computational approach.

## Key findings

- Universal logarithmic coefficient of -61/45 for entanglement entropy.
- Equivalence of graviton entropy to scalar entropy after mode subtraction.
- Agreement with mutual information calculations.

## Abstract

We compute the entanglement entropy of a massless spin $2$ field in a sphere in flat Minkowski space. We describe the theory with a linearized metric perturbation field $h_{\mu\nu}$ and decompose it in tensor spherical harmonics. We fix the gauge such that a) the two dynamical modes for each angular momentum decouple and have the dynamics of scalar spherical modes, and b) the gauge-fixed field degrees of freedom inside the sphere represent gauge invariant operators of the theory localized in the same region. In this way the entanglement entropy turns out to be equivalent to the one of a pair of free massless scalars where the contributions of the $l=0$ and $l=1$ modes have been subtracted. The result for the coefficient of the universal logarithmic term is $-61/45$ and coincides with the one computed using the mutual information.