Positive-gravitational-energy proof from complex variables?

The teleparallelism equivalent of Einstein's theory of general relativity is a physically important subcase of the quadratic Poincaré gauge theory. Within this Riemann-Cartan framework, new complex variables resembling those of Ashtekar can be generated already on the Lagrangian level via Chern-Simons-type boundary terms. As a result, the field equations boil down to a covariant Gauss law with respect to a Sen-type connection and the complexified Lagrangian becomes purely quadratic in the new translational field momenta. Moreover, the gravitational Hamiltonian resulting from a 3 + 1 decomposition of these new variables becomes non-negative, provided a certain elliptic gauge holds for the tangential frame.