Spontaneous scalarization of charged black holes at the approach to extremality

Abstract

We study static, spherically symmetric and electrically charged black hole solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very similar to the uncharged case, black holes undergo spontaneous scalarization for sufficiently large scalar-tensor coupling γ -a phenomenon attributed to a tachyonic instability of the scalar field system. While in the uncharged case, this effect is only possible for positive values of γ, we show that for sufficiently large values of the electric charge Q two independent domains of existence in the γ-Q-plane appear : one for positive γ and one for negative γ. We demonstrate that this new domain for negative γ exists because of the fact that the near-horizon geometry of a nearly extremally charged black hole is AdS 2 × S 2 . This new domain appears for electric charges larger than approximately 74% of the extremal charge. For positive γ we observe that a singularity with diverging curvature invariants forms outside the horizon when approaching extremality.

Theory-agnostic framework for dynamical scalarization of compact binaries

“…Despite its simplicity, the effective action (7) is theory agnostic, in the sense that it is constructed assuming only the scalar-inversion symmetry and that the nonrotating compact object hosts such a mode; in particular, it should hold for the cases studied in Refs. [16,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and similar work to come. We emphasize that strong-field UV physics at the bodyscale is parametrized through the numerical coefficients c ... , which can be matched to a specific theory and compact object, or be constrained directly from observations (analogous to tidal parameters [9,52]).…”

“…For a stable scalarized equi-librium configuration to exist, this instability must saturate in the nonlinear regime [55]. These two conditionsthe existence of a tachyonic instability and its eventual saturation-are satisfied in all of the theories discussed previously [16,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The only difference between these theories is the form of m 2 eff ; for example, in ST theories m 2 eff depends on the stress-energy tensor, while in ESTGB it depends on the Gauss-Bonnet invariant.…”

“…Specifically, we investigate the non-linear scalarization of nonrotating compact objects (BHs and NSs), which arises from spontaneous symmetry breaking of an additional scalar component of gravity [17,18]. Spontaneous scalarization-the scalarization of a single, isolated object-has been found in several scalar extensions of GR, including massless [19][20][21][22][23][24][25] and massive [26][27][28] scalar-tensor (ST) theories and extended scalar-tensor-Gauss-Bonnet (ESTGB) theories [29][30][31][32][33][34]. Similar phenomena can also occur for vector [35,36], gauge [16], and spinor [37] fields.…”

Black hole spontaneous scalarisation with a positive cosmological constant

“…As a result, the GR solutions are unstable against scalar perturbations in regions where the source term is significant, dynamically developing scalar hair, i.e. spontaneously scalarising.Various expressions of I have been considered in the literature, that fall roughly into two types: I is a geometric invariant, such as the Gauss-Bonnet invariant [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], the Ricci scalar for non-conformally invariant BHs [37], or the Chern-Simons invariant [38]; or I is a "matter" invariant, such as the Maxwell F 2 term [39][40][41][42][43][44][45][46]. This phenomenon is actually not exclusive of scalar fields [47].…”

Spontaneous scalarization of boson stars

“…The first studies of this type have been done in the conformally coupled scalar field case [22] as well as for the f (φ)G case [31]. The studies were extended to discuss the approach to the extremal limit in [32] and it was demonstrated that scalarized black holes can exist for both signs of the scalar-tensor coupling due to the fact that G becomes negative close to the horizon when approaching extremality. Since the electromagnetic field can source the scalar field when non-minimally coupled, charged black holes can also carry scalar hair without scalar-tensor coupling [33,34].The first study of neutron stars in scalar-tensor gravities has been done in [35].…”