Abstract
In the presence of appropriate non-minimal couplings between a scalar field and the curvature squared Gauss–Bonnet (GB) term, compact objects such as neutron stars and black holes (BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The non-minimal coupling functions that allow this mechanism are, however, always postulated ad hoc. Here, we point out that families of such functions naturally emerge in the context of Higgs–Chern–Simons gravity models, which are found as dimensionally descents of higher dimensional, purely topological, Chern–Pontryagin non-Abelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions in a particular Einstein-GB-scalar field model, whose coupling is obtained from this construction, pointing out novel features and caveats thereof. The possibility of vectorization is also discussed, since this construction also originates vector fields non-minimally coupled to the GB invariant.
Highlights
The General Relativity (GR) black holes (BHs) solutions are unstable against scalar perturbations in regions where the source term is significant, leading to BH scalar hair growth
To the best of our knowledge, a common feature of models allowing for BH scalarization is that the origin of the term f (φ) LGB in (1), and, in particular, the choice of the coupling function f (φ) is ad hoc, missing a well motivated origin (The coupling function f (φ) = e−φ naturally appears in the string theory context, when including first-order α0 corrections
This paper is organized as follows: in Section 2, we review the basic features of the model in [41], in particular its derivation starting with a Chern–Pontryagin (CP) density in D = 8 dimensions
Summary
To the best of our knowledge, a common feature of models allowing for BH scalarization is that the origin of the term f (φ) LGB in (1), and, in particular, the choice of the coupling function f (φ) is ad hoc, missing a well motivated origin (The coupling function f (φ) = e−φ naturally appears in the string theory context, when including first-order α0 corrections (with φ the dilaton field). Both generic configurations (with a value of the scalar field which does not approach asymptotically the ground state) and scalarized BHs are discussed; a perturbative (analytic) solution is derived in the former case.
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