Mixed scalarization of charged black holes: from spontaneous to non-linear scalarization

Scalarized black holes (BH) have been shown to form dynamically in extended-scalar-tensor theories, either through spontaneous scalarization -- when the BH is unstable against linear perturbations -- or through a non-linear scalarization. In the latter, linearly stable BHs can ignite scalarization when sufficiently perturbed. These phenomena are, however, not incompatible and mixed scalarization is also possible. The objective of this work is twofold: first, study mixed scalarization on a family of Einstein-Maxwell-scalar models; and second, study the effect of the counter scalarization that occurs when one of the coupling parameters has a sign opposite to the one that generates scalarization. Both objectives are addressed by constructing and examining the mixed scalarization's domain of existence. An overall dominance of the spontaneous scalarization over the non-linear scalarization is observed. Thermodynamically, an entropical preference for mixed over the standard scalarization (spontaneous or non-linear) exists. In the presence of counter scalarization, a quench of the scalarization occurs, mimicking the effect of a scalar particle's mass/positive self-interaction term.Comment: 14 pages, 5 figure

The spooky ghost of vectorization

An interesting mechanism for the formation of hairy black holes occurs when a vector field, non-minimally coupled to a source term, grows from a perturbation of the vacuum black hole, \textit{aka} vectorization. Its study has, however, been lacking, in part due to the constant threat of ghost instabilities that have plagued vector fields. In this work, we show evidence that, in a generic family of extended-vector-tensor theories where the vector field is non-minimally coupled to the model's invariant (source term), a spherically symmetric, vectorized black hole always suffers from ghost instabilities. These ultimately turn the process of vectorization astrophysically unviable.Comment: 12 page

A Sun-like star orbiting a boson star

The high-precision astrometric mission GAIA recently reported the remarkable discovery of a Sun-like star closely orbiting a dark object, with a semi-major axis and period of $1.4\, \rm{AU}$ and $187.8$ days respectively. While the plausible expectation for the central dark object is a black hole, the evolutionary mechanism leading to the formation of such a two-body system is highly challenging. Here, we challenge the scenario of a central black hole and show that the observed orbital dynamics can be explained under fairly general assumptions if the central dark object is a stable clump of bosonic particles of spin-0, or spin-1, known as a boson star. We further explain how future astrometric measurements of similar systems will provide an exciting opportunity to probe the fundamental nature of compact objects and test compact alternatives to black holes.Comment: 11 pages, 4 figures. Comments are very welcom

Effects of mass and self-interaction on nonlinear scalarization of scalar-Gauss-Bonnet black holes

It was recently found that in certain flavours of scalar-Gauss-Bonnet gravity linearly stable bald black holes can co-exist with stable scalarized solutions. The transition between both can be ignited by a large nonlinear perturbation, thus the process was dubbed non-linear scalarization, and it happens with a jump that leads to interesting astrophysical implications. Generalizing these results to the case of nonzero scalar field potential is important because a massive self-interacting scalar field can have interesting theoretical and observational consequences, e.g. reconcile scalar-Gauss-Bonnet gravity with binary pulsar observation, stabilize black hole solutions, etc. That is why in the present paper, we address this open problem. We pay special attention to the influence of a scalar field mass and self-interaction on the existence of scalarized phases and the presence of a jump between stable bald and hairy back holes. Our results show that both the addition of a mass and positive self-interaction of the scalar field result in suppression or quenching of the overall scalarization phenomena. A negative scalar field self-interaction results in an increase of the scalarization. The presence and the size of the jump, though, are not so sensitive to the scalar field potential.Comment: 18 pages, 9 figure

Spontaneous vectorization of electrically charged black holes

In this work, we generalise the spontaneous scalarization phenomena in Einstein-Maxwell-Scalar models to a higher spin field. The result is an Einstein-Maxwell-Vector model wherein a vector field is non-minimally coupled to the Maxwell invariant by an exponential coupling function. We show that the latter guarantees the circumvention of an associated no-hair theorem when the vector field has the form of an electric field. Different than its scalar counterpart, the new spontaneously vectorized ReissnerNordstr¨om (RN) black holes are, always, undercharged while being entropically preferable. The solution profile and domain of existence are presented and analysed.publishe

Einstein-Maxwell-scalar black holes: the hot, the cold and the bald

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function $f(\phi)$, between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordstr\"om (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: $f(\Phi) = 1+\alpha \Phi ^4$. The domain of existence of the scalarised BHs, for fixed $\alpha$, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myer-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.Comment: 12 pages, 6 figure

Scalaroca stars: coupled scalar-Proca solitons

We construct and explore the physical properties of \textit{scalaroca stars}: spherically symmetric solitonic solutions made of a complex scalar field $\Phi$ and a complex Proca field $A^\mu$. We restrict our attention to configurations in which both fields are in the fundamental state and possess an equal mass, focusing on the cases when ($i$) the scalar and Proca fields are (non--linearly) super--imposed and do not interact with each other; and ($ii$) the scalar and Proca fields interact through the term $\alpha |\Phi| ^2 A^\mu A_\mu$. The solutions are found numerically for the non--interacting case ($\alpha=0$) as well as for both signs of the interaction coupling constant $\alpha$. While pure ($i.e.$ single--field) Proca/scalar boson stars are the most/least massive for weakly--interacting fields, one can obtain more massive solutions for a sufficiently strong interaction. Besides, in the latter case, solutions can be either in a synchronized state -- in which both fields have the same frequency -- or in a non--synchronized state. In addition, we observe that the coupling between the two fields allows solitonic solutions with a real scalar field. We further comment on the possibility of spontaneous scalarization and vectorization of the interacting solitonic solution.Comment: 21 pages, 13 figures, this project was started before the recently published work ArXiv:2304.0801

Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms

Virial (aka scaling) identities are integral identities that are useful for a variety of purposes in nonlinear field theories, including establishing no-go theorems for solitonic and black hole solutions, as well as for checking the accuracy of numerical solutions. In this paper, we provide a pedagogical rationale for the derivation of such integral identities, starting from the standard variational treatment of particle mechanics. In the framework of one-dimensional (1D) effective actions, the treatment presented here yields a set of useful formulas for computing virial identities in any field theory. Then, we propose that a complete treatment of virial identities in relativistic gravity must take into account the appropriate boundary term. For General Relativity this is the Gibbons-Hawking-York boundary term. We test and confirm this proposal with concrete examples. Our analysis here is restricted to spherically symmetric configurations, which yield 1D effective actions (leaving higher-D effective actions and in particular the axially symmetric case to a companion paper). In this case, we show that there is a particular “gauge” choice, i.e. a choice of coordinates and parametrizing metric functions, that simplifies the computation of virial identities in General Relativity, making both the Einstein-Hilbert action and the Gibbons-Hawking-York boundary term noncontributing. Under this choice, the virial identity results exclusively from the matter action. For generic “gauge” choices, however, this is not the case.publishe

The imitation game: Proca stars that can mimic the Schwarzschild shadow

Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact - i.e., possess LRs - but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions are considered. However, an effective shadow can arise in a different way: if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike geodesics (located at $r_{\rm ISCO}=6M$ for a Schwarzschild BH of mass M), the accretion flow morphology around BHs is mimicked and an effective shadow arises in an astrophysical environment. Even though spherical BSs may accommodate stable timelike circular orbits all the way down to their centre, we show the angular velocity along such orbits may have a maximum away from the origin, at $R_{\Omega}$; this scale was recently observed to mimic the BH's ISCO in some scenarios of accretion flow. Then: (i) for free scalar fields or with quartic self-interactions, $R_{\Omega}\neq 0$ only for perturbatively unstable BSs; (ii) for higher scalar self-interactions, e.g. axionic, $R_{\Omega}\neq 0$ is possible for perturbatively stable BSs, but no solution with $R_{\Omega}=6M$ was found in the parameter space explored; (iii) but for free vector fields, yielding Proca stars (PSs), perturbatively stable solutions with $R_{\Omega}\neq 0$ exist, and indeed $R_{\Omega}=6M$ for a particular solution. Thus, dynamically robust spherical PSs can mimic the shadow of a (near-)equilibrium Schwarzschild BH with the same M, in an astrophysical environment, despite the absence of a LR, at least under some observation conditions, as we confirm by comparing the lensing of such PSs and Schwarzschild BHs.Comment: Abstract abridged due to arXiv length limit; 22 pages, 9 figure

Charged black holes with axionic-type couplings: classes of solutions and dynamical scalarization

We consider an augmented Einstein-Maxwell-scalar model including an axionic-type coupling between the scalar and electromagnetic field. We study dyonic black hole solutions in this model. For the canonical axionic coupling emerging from high energy physics, all charged black holes have axion hair. We present their domain of existence and investigate some physical properties. For other axionic-type couplings, two classes of black hole solutions may coexist in the model: scalar-free Reissner-Nordström black holes and scalarized black holes. We show that in some region of the parameter space the scalar-free solutions are unstable. Then, there is nonuniqueness since new scalarized black hole solutions with the same global charges, which are entropically preferred over the scalar-free solutions and, moreover, emerge dynamically from the instability of the former, also exist.publishe