GRAVITATIONAL DYNAMICS WITH LORENTZ CHERN-SIMONS TERMS

We consider corrections to Einstein gravity arising from the inclusion of Lorentz Chern-Simons terms, as well as Gauss-Bonnet terms, in a theory containing dilatons and Kalb-Ramond axions as in string theory. We show that all four-dimensional space-times with a maximally symmetric two-dimensional subspace have vanishing Lorentz Chern-Simons terms, which do not contribute to gravitational equations of motion or Bianchi identities. In addition, space-times conformally related to such have exact Lorentz Chern-Simons terms. This greatly simplifies the equations of motion for space-times of this form, such as Robertson-Walker and Schwarzschild. On the contrary, we show that for both the Kerr metric, and the Bianchi IX metric, Lorentz Chern-Simons terms cannot be neglected and lead to a non-trivial modification of the gravitational equations of motion, as well as the Bianchi identity for the Kalb-Ramond field strength, dH = tr R AND R not-equal 0.