Seven-Dimensional Gravity with Topological Terms

Abstract

We construct new seven-dimensional gravity by adding two topological terms to the Einstein-Hilbert action. For certain choice of the coupling constants, these terms may be related to the R^4 correction to the 3-form field equation of eleven-dimensional supergravity. We derive the full set of the equations of motion. We find that the static spherically-symmetric black holes are unmodified by the topological terms. We obtain squashed AdS_7, and also squashed seven spheres and Q^{111} spaces in Euclidean signature.