The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics
  We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter. 
J. Fernando Barbero G., Alfredo Tiemblo, and Romualdo Treseguerres