Timelike surfaces in Lorentz covariant loop gravity and spin foam models

We apply a recently developed canonical formulation of general relativity, which possesses explicit covariance with respect to Lorentz transformations in the tangent space, to describe the case of a timelike foliation of spacetime. Assuming that such a theory based on a timelike foliation makes sense, we derive the spectrum of the area operator of a two-dimensional surface in the framework of the loop quantization. Its different branches are naturally associated with spacelike and timelike surfaces. The results are compared with the predictions of Lorentzian (Baffett-Crane) spin foam models. A restriction of the representations labelling spin networks leads to perfect agreement between the states as well as the area spectra in the two approaches.