We construct new seven-dimensional gravity by adding two topological terms to the Einstein-Hilbert action. For a certain choice of the coupling constants, these terms exist naturally in seven-dimensional gauged supergravity from the $S^4$ reduction of eleven-dimensional supergravity with the $R^4$ corrections. 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 ${\mathrm{AdS}}_7$, and also squashed seven spheres and $Q^{111}$ spaces in Euclidean signature.

• Received 6 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.085016