Chern-Simons modification of general relativity

@article{Jackiw2003ChernSimonsMO,
  title={Chern-Simons modification of general relativity},
  author={Roman Jackiw and S. Y. Pi},
  journal={Physical Review D},
  year={2003},
  volume={68},
  pages={104012}
}
General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild… 
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