Seven-Dimensional Gravity with Topological Terms

TL;DR

This paper develops a new seven-dimensional gravity theory incorporating topological terms, explores its solutions including black holes and squashed geometries, and relates these to supergravity corrections.

Contribution

It introduces a novel seven-dimensional gravity model with topological terms linked to supergravity R^4 corrections and derives its equations of motion.

Findings

Static black holes remain unchanged by topological terms

Constructed squashed AdS_7 and sphere solutions

Connected topological terms to eleven-dimensional supergravity

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.