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Abstract Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function $$f(\phi )$$ f ( ϕ ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, $$f(\phi )=1+\alpha \phi ^4$$ f ( ϕ ) = 1 + α ϕ 4 (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

Abstract We calculate the quasinormal modes of static spherically symmetric dilatonic Reissner–Nordström black holes for general values of the electric charge and of the dilaton coupling constant. The spectrum of quasinormal modes is composed of five families of modes: polar and axial gravitational-led modes, polar and axial electromagnetic-led modes, and polar scalar-led modes. We make a quantitative analysis of the spectrum, revealing its dependence on the electric charge and on the dilaton coupling constant. For large electric charge and large dilaton coupling, strong deviations from the Reissner–Nordström modes arise. In particular, isospectrality is strongly broken, both for the electromagnetic-led and the gravitational-led modes, for large values of the charge.

Individual differences in children’s prosocial behaviors, including their willingness to give up something of value for the benefit of others, are rooted in physiological and environmental processes. In a sample of 4-year-old children, we previously found evidence that flexible changes in respiratory sinus arrhythmia (RSA) were linked to donation behavior, and that these physiological patterns may support greater sensitivity to the positive effects of compassionate parenting on donation behavior. The current study focused on a follow-up assessment of these children at age 6. First, we examined the stability of individual differences in donation behavior and related parasympathetic nervous system (PNS) activity from age 4 to 6. Second, we examined associations between donation behavior and RSA at 6 years. Third, we examined whether the association between children’s RSA and donation behavior at age 6 varied depending on mothers’ compassionate love. We found low to modest stability in donation behavior and RSA reactivity from age 4 to 6. These findings provide preliminary evidence that stable individual differences in altruism, as reflected by generosity, and in some aspects of parasympathetic functioning during opportunities to be prosocial, emerge in childhood. In addition, we found that some of the same associations between donation behavior, RSA, and compassionate love that we previously observed in children at 4 years of age continued to be evident 2 years later at age 6. Greater decreases in RSA when given the opportunity to donate were associated with children donating more of their own resources which, in turn, were associated with greater RSA recovery after the task. Lastly, mothers’ compassionate love was positively associated with donation behavior in children who demonstrated stronger decreases in RSA during the task; compassionate parenting and RSA reactivity may serve as external and internal supports for prosociality that build on each other. Taken together, these findings contribute to the perspectives that individual differences in altruistic behaviors are intrinsically linked to healthy vagal flexibility, and that biopsychosocial approaches provide a useful framework for examining and understanding the environmental and physiological processes underlying these individual differences.

We demonstrate that rotating matter sets the throat of an Ellis wormhole into rotation, allowing for wormholes which possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. We analyze the properties of this new type of rotating wormholes and show that the wormhole geometry can change from a single throat to a double throat configuration. We further discuss the ergoregions and the lightring structure of these wormholes.

In this work we present some new results obtained in a study of the phase diagram of charged compact boson stars in a theory involving a complex scalar field with a conical potential coupled to a U(1) gauge field and gravity. We here obtain new bifurcation points in this model. We present a detailed discussion of the various regions of the phase diagram with respect to the bifurcation points. The theory is seen to contain rich physics in a particular domain of the phase diagram.

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.