  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.
