Gravitational Chern–Simons, and Chern–Simons Gravity in All Dimensions

Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

“…The HCSG models in [41,42] are particular examples of gauge theories of gravity, and follow the spirit (and the general framework) in [43][44][45][46][47][48], with the usual identification of the spin-connection and the Riemann curvature with the YM connection and curvature. As a new feature, an extra-Higgs-like scalar and a vector field occur in the four dimensional action for the specific model studied in this work.…”

“…For completeness, in this section, we briefly review the flavour of the results in Refs. [41,42], which proposes a general framework for the construction of such HCSG models.…”

“…this is a topological theory). However, the approach in [41,42] (see also the Refs. [49,50] and the Appendix A of Ref.…”

“…For both the Chern-Simons and Higgs-Chern-Simons cases, the final step is the (standard) prescription for the passage to gravity, the spin-connection being identified with the YM connection. In the latter case, this prescription must be extended by the corresponding elements pertaining to the Higgs sector, which generically result in extra frame-vector fields, apart from the scalar field(s) [41,42]. By analogy to the standard Chern-Simons gravities (which exist in odd-dimensions only [52]), the resulting models are dubbed HCSG.…”

“…Despite this fact, some features found for scalarized BHs occur also in this case, a relevant example being the appearance of repulsive effects for static, spherically symmetric solutions [40]). The main purpose of this work is the study of the basic properties of the BH solutions in a model where the interaction term f (φ)L GB emerges naturally from a Higgs-Chern-Simons gravity (HCSG), originally proposed in [41,42]. The corresponding expression of the coupling function is…”