  We generalize a model recently proposed for Euclidean quantum gravity to the
case of Lorentzian signature. The main features of the Euclidean model are
preserved in the Lorentzian one. In particular, the boundary Hilbert space
matches the one of SU(2) loop quantum gravity. As in the Euclidean case, the
model can be obtained from the Lorentzian Barrett-Crane model from a flipping
of the Poisson structure, or alternatively, by adding a topological term to the
action and taking the small Barbero-Immirzi parameter limit.
