  In this paper we study the entanglement entropy in the CFT$_2$, whose gravity
dual is AdS$_3$ spacetime with a Chern-Simons term. Using the generalized
Rindler method, we obtain the Rindler transformation in the two-dimensional
planar CFT and compute the entanglement entropy of the CFT with gravitational
anomalies. The conditions under which the entanglement entropy may have
anomalous contributions is also discussed. In addition, we present a relatively
general form of the Rindler AdS metric and compute its thermal entropy, which
agrees with the entanglement entropy in the field theory. Moreover, we utilize
the conformal transformation, which maps a cylinder to a plane, to compute the
entanglement entropy of the CFT residing on a cylinder, as well as the
entanglement entropy of the CFT at finite temperature on a plane. The
corresponding contribution of the Chern-Simons term in gravity to the black
hole thermal entropy is also obtained from this approach. These results are
important for further understandings of the two-dimensional CFT with
gravitational anomalies.
