  We study the entanglement entropy in a relativistic quantum field theory for
regions which are not included in a single spatial hyperplane. This geometric
configuration cannot be treated with the Euclidean time method and the replica
trick. Instead, we use a real time method to calculate the entropy for a
massive free Dirac field in two dimensions in some approximations. We find some
specifically relativistic features of the entropy. First, there is a large
enhancement of entanglement due to boosts. As a result, the mutual information
between relatively boosted regions does not vanish in the limit of zero volume
and large relative boost. We also find extensivity of the information in a
deeply Lorentzian regime with large violations of the triangle inequalities for
the distances. This last effect is relevant to an interpretation of the amount
of entropy enclosed in the Hawking radiation emitted by a black hole.
