  According to the Ryu-Takayanagi prescription, the entanglement entropy of
subsystems in the boundary conformal field theory (CFT) is proportional to the
area of extremal surfaces in bulk asymptotically Anti-de Sitter (AdS)
spacetimes. The flat-space limit of these surfaces is not well defined in the
generic case. We introduce a new curve in the three-dimensional asymptotically
AdS spacetimes with a well-defined flat-space limit. We find this curve by
using a new vector, which is vanishing on it and is normal to the bulk modular
flow of the original interval in the two-dimensional CFT. The flat-space limit
of this new vector is well defined and gives rise to the bulk modular flow of
the corresponding asymptotically flat spacetime. Moreover, after Rindler
transformation, this new vector is the normal Killing vector of the BTZ inner
horizon. We reproduce all known results about the holographic entanglement
entropy of Bondi-Metzner-Sachs invariant field theories, which are dual to the
asymptotically flat spacetimes.
