  With an aim towards understanding the time-dependence of entanglement entropy
in generic quantum field theories, we propose a covariant generalization of the
holographic entanglement entropy proposal of hep-th/0603001. Apart from
providing several examples of possible covariant generalizations, we study a
particular construction based on light-sheets, motivated in similar spirit to
the covariant entropy bound underlying the holographic principle. In
particular, we argue that the entanglement entropy associated with a specified
region on the boundary in the context of the AdS/CFT correspondence is given by
the area of a co-dimension two bulk surface with vanishing expansions of null
geodesics. We demonstrate our construction with several examples to illustrate
its reduction to the holographic entanglement entropy proposal in static
spacetimes. We further show how this proposal may be used to understand the
time evolution of entanglement entropy in a time varying QFT state dual to a
collapsing black hole background. Finally, we use our proposal to argue that
the Euclidean wormhole geometries with multiple boundaries should be regarded
as states in a non-interacting but entangled set of QFTs, one associated to
each boundary.
