Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term

We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e., in $D=4k-1$). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a seven-dimensional theory in which a purely gravitational Chern-Simons term is added to the Einstein-Hilbert Lagrangian in $D=7$ dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.