Key points are not available for this paper at this time.
It has recently been shown that one can reformulate general relativity in such a way that the canonical variables of the theory resemble those of Yang-Mills theory and the freedom in performing internal rotations on tetrads is completely analogous to the freedom in performing local gauge transformations in Yang-Mills theory. This reformulation is used to carry over, in the canonical framework, the analysis of the θ vacua and the associated CP problem from Yang-Mills theory to general relativity. The analysis depends only on certain qualitative features of general relativity—shared by other field theories of gravitation such as supergravity—and is insensitive to the details of the theory as well as of the way in which the canonical quantization program may be eventually completed.
Ashtekar et al. (Mon,) studied this question.