Abstract
We consider a modification of the standard Einstein theory in four dimensions, alternative to R. Jackiw and S.-Y. Pi, Phys. Rev. D 68, 104012 (2003), since it is based on the first-order (Einstein-Cartan) approach to general relativity, whose gauge structure is manifest. This is done by introducing an additional topological term in the action which becomes a Lorentz-violating term by virtue of the dependence of the coupling on the space-time point. We obtain a condition on the solutions of the Einstein equations, such that they persist in the deformed theory, and show that the solutions remarkably correspond to the classical solutions of a collection of independent -dimensional (topological) Chern-Simons gravities. Finally, we study the relation with the standard second-order approach and argue that they both coincide to leading order in the modulus of the Lorentz-violating vector field.
- Received 4 January 2008
DOI:https://doi.org/10.1103/PhysRevD.78.025002
©2008 American Physical Society