Special orthonormal frames and Dirac spinors in Kerr geometry

Since Einstein's general theory of relativity for gravity is a frame independent theory, it has the freedom of choosing an orthonormal frame. I can use a gauge condition to select a preferred orthonormal frame for some gravitational systems. The gauge condition selects a special orthonormal frame (SOF). This special orthonormal frame has application in particular to a positive energy proof and energy localization for a gravitational system. The gauge condition is related to the solution of the Dirac equation; by solving the Dirac equation we can determine a special orthonormal frame. However, in curved spacetime the solution of Dirac equation is highly nontrivial.