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In this paper, we study the spontaneous scalarization of an extended, self-gravitating system which is static, cylindrically symmetric and possesses electromagnetic fields. We demonstrate that a real massive scalar field condenses on this Melvin magnetic universe solution when introducing a non-minimal coupling between the scalar field and (a) the magnetic field and (b) the curvature of the space-time, respectively. We find that in both cases, the solutions exist on a finite interval of the coupling constant and that solutions with a number of nodes $k$ in the scalar field exist. For case (a) we observe that the intervals of existence are mutually exclusive for different $k$.
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Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection gravity by setting up scalars and connection configurations instead of metric. Since the matter sector is not straightforward to conceive without a metric, we invoke cosmological fluids in terms of their one-form velocity in the volume element of the invariant action. This leads to gravitational equations with a perfect fluid source and a generated metric, which are expected to produce reasonable deviations from general relativity in the strong-field regime. As a relevant application, we study spontaneous scalarization mechanism and show that the Damour-Esposito-Far`{e}se model arises in a certain class of scalar-connection gravity. Furthermore, we investigate a general study in which the present framework becomes distinguishable from the famed scalar-tensor theories.
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $overline{psi}psi=0$ with non-vanishing bi-linear pseudo-scalar $ioverline{psi}gamma^5psi ot=0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.
Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. In this paper, we identify all of the terms in the Horndeski action that contribute to the (effective) mass term in the linearized equations and, hence, can cause or contribute to the tachyonic instability that triggers scalarization.
We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the $(alpha {cal R} + gamma {cal G}) phi^2$ scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has harmonic time dependence, while their space-time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling $alpha$ and $gamma$, respectively. This is, in particular, true for boson stars that are {it a priori} stable with respect to decay into individual bosonic particles. A fundamental difference between the $alpha$- and $gamma$-scalarization exists, though: while we find an interval in $alpha > 0$ for which boson stars can {it never} be scalarized when $gamma=0$, there is no restriction on $gamma eq 0$ when $alpha=0$. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
We study static and spherically symmetric charged stars with a nontrivial profile of the scalar field $phi$ in Einstein-Maxwell-scalar theories. The scalar field is coupled to a $U(1)$ gauge field $A_{mu}$ with the form $-alpha(phi)F_{mu u}F^{mu u}/4$, where $F_{mu u}=partial_{mu}A_{ u}-partial_{ u} A_{mu}$ is the field strength tensor. Analogous to the case of charged black holes, we show that this type of interaction can induce spontaneous scalarization of charged stars under the conditions $({rm d}alpha/{rm d}phi) (0)=0$ and $({rm d}^2alpha/{rm d}phi^2) (0)>0$. For the coupling $alpha (phi)=exp (-beta phi^2/M_{rm pl}^2)$, where $beta~(<0)$ is a coupling constant and $M_{rm pl}$ is a reduced Planck mass, there is a branch of charged star solutions with a nontrivial profile of $phi$ approaching $0$ toward spatial infinity, besides a branch of general relativistic solutions with a vanishing scalar field, i.e., solutions in the Einstein-Maxwell model. As the ratio $rho_c/rho_m$ between charge density $rho_c$ and matter density $rho_m$ increases toward its maximum value, the mass $M$ of charged stars in general relativity tends to be enhanced due to the increase of repulsive Coulomb force against gravity. In this regime, the appearance of nontrivial branches induced by negative $beta$ of order $-1$ effectively reduces the Coulomb force for a wide range of central matter densities, leading to charged stars with smaller masses and radii in comparison to those in the general relativistic branch. Our analysis indicates that spontaneous scalarization of stars can be induced not only by the coupling to curvature invariants but also by the scalar-gauge coupling in Einstein gravity.
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