Gravitational Chern–Simons, and Chern–Simons gravity in all dimensions

Abstract

The construction of Chern–Simons gravities (CSG) and gravitational Chern–Simons densities (GCS) are considered. Since both these are definied the non-Abelian (nA) Chern–Simons densities (CS) in the appropriate representations, and the latter are defined only in odd dimensions, so are the CSG and the GCS. To overcome this restriction, it is proposed that instead of employing nA CS densities, the Higgs–CS (HCS) densities are employed, the latter being defined in all dimensions and hence leading to their gravitational counterparts, HCS-Gravity (HCSG) Lagrangians and gravitational-HCS (GHCS) densities, not all of them restricted to odd dimensions. A detailed definition for a GHCS density in 3 + 1 dimensions is presented, and, a new result in black hole solutions in CSG gravity models in all odd dimensions is presented.