This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift and the inertia of these objects and compare them with known data.
The Einstein-Klein-Gordon Lagrangian is supplemented by a non-minimal coupling of the scalar field to specific geometric invariants : the Gauss-Bonnet term and the Chern-Simons term. The non-minimal coupling is chosen as a general quadratic polynomial in the scalar field and allows -depending on the parameters -for large families of hairy black holes to exist. These solutions are characterized, namely, by the number of nodes of the scalar function. The fundamental family encompasses black holes whose scalar hairs appear spontaneously and solutions presenting shift-symmetric hairs. When supplemented by a an appropriate potential, the model possesses both hairy black holes and non-topological solitons : boson stars. These latter exist in the standard Einstein-Klein-Gordon equations; it is shown that the coupling to the Gauss-Bonnet term modifies considerably their domain of classical stability.Abandonning the hypothesis of shift-symmetry, several groups [12], [13], [14] considered during the past years, new types of coupling terms between a scalar field and specific geometric invariants (essentially the Gauss-Bonnet term). In these models the occurrence of hairy black holes results from an unstable mode of the scalar field equation in the background of a vacuum metric (the probe limit). The interacting term of the scalar field with the curvature invariant plays a role of potential and the coupling constant the role of a spectral parameter. By continuity, the hairy black holes then exist as solutions of the full system. It is used to say that the hairy black holes appear through a spontaneous scalarization for a sufficiently large value of the coupling constant.In the present paper we will consider a model of scalar-tensor gravity encompassing the theories presenting a spontaneous scalarization and the shift-symmetry property. Families of classical solutions whose pattern extrapolates smoothly between shift-symmetric hairy black holes and spontaneous scalarized ones will be constructed . The type of structure found holds when coupling the scalar field to the Gauss-Bonnet invariant and to the Einstein-Chern-Simons invariant as well. All black holes solutions found are supported by the non-minimal coupling between the scalar field and the curvature invariant; however the field equations admit other types of solutions: boson stars. These regular solutions exist with a minimal coupling of scalar field to gravity but it will be shown that the non minimal coupling has important consequences on their stability properties.The paper is organized as follow : in Sect. 2 we present the model to be studied. Namely the Einstein-Klein-Gordon Lagrangian extended by a non-minimal coupling. We discuss the spherically symmetric ansatz and the general form of the field equations. Sect. 3 is devoted to the presentation of the hairy black holes occurring in the model. The boson stars are presented in Sect. 4 with an emphasis on the influence of the non-minimal coupling of the spectrum of the solutions. Conclusions are drawn in Sect. 5. S...
Black holes play a crucial role in the understanding of the gravitational interaction. Through the direct observation of the shadow of a black hole by the event horizon telescope and the detection of gravitational waves of merging black holes we now start to have direct access to their properties and behaviour, which means the properties and behaviour of gravity. This further raised the demand for models to compare with those observations. In this respect, an important question regarding black holes properties is to know if they can support “hairs”. While this is famously forbidden in general relativity, in particular for scalar fields, by the so-called no-hair theorems, hairy black holes have been shown to exist in several class of scalar-tensor theories of gravity. In this article we investigate the existence of scalarized black holes in scalar-torsion theories of gravity. On one hand, we find exact solutions for certain choices of couplings between a scalar field and the torsion tensor of a teleparallel connection and certain scalar field potentials, and thus proof the existence of scalarized black holes in these theories. On the other hand, we show that it is possible to establish no-scalar-hair theorems similar to what is known in general relativity for other choices of these functions.
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schrödinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is extended for one-dimensional Hamiltonians with a non-usual kinetic part. The validity of the approach is tested with a Hamiltonian containing a relativistic kinetic energy operator.
The Einstein-Gauss-Bonnet gravity in five dimensions is extended by scalar fields and the corresponding equations are reduced to a system of non-linear differential equations. A large family of regular solutions of these equations is shown to exist. Generically, these solutions are spinning black holes with scalar hairs. They can be characterized (but not uniquely) by an horizon and an angular velocity on this horizon. Taking particular limits the black holes approach boson star or become extremal, in any case the limiting configurations remain hairy.
Einstein gravity supplemented by a scalar field non-minimally coupled to a Gauss-Bonnet term provides an example of model of scalar-tensor gravity where hairy black holes do exist. We consider the classical equations within a metric endowed with a NUT-charge and obtain a two-parameter family of nutty-hairy black holes. The pattern of these solutions in the exterior and the interior of their horizon is studied in some details. The influence of both -the hairs and the NUT-charge -on the lightlike and timelike geodesics is emphasized.of the Schwarzschild black hole characterized by a new parameter : the so-called NUT charge n. Although purely analytic, the NUT space-time presents peculiarities [16,17] that makes that its physical interpretation is, till now, a matter of debate. In particular, the solution presents a Misner string singularity on the polar axis and the corresponding space-time contains closed timelike curves. Various arguments rehabilitating space-time with a NUT charge are proposed in [18]. In spite of the difficulty of finding a global definition of the NUT space-time, the solution possesses many remarquable properties, namely : (i) like the Kerr solution, it is stationary but non-static due to non-vanishing g tϕ metric terms ; (ii) it can be extended analytically (i.e. without curvature singularity) in the interior region by means of a TAUB solution.Likely for these reasons, several authors (see namely [19,20]) have considered the NUT parameter as a possible ingredient of some astrophysical object and have studied its effect on geodesics in NUT space-times. Another application of the NUT parameter was proposed recently in [21] to obtain families of non-trivial, spherically symmetric solutions of the Einstein-Chern-Simons gravity coupled to a scalar field. Such a construction was possible by taking advantage of the stationary character of the underlying metric.In this paper we extend the construction of the hairy black holes of [10] by including a NUT parameter in the metric. We show that Nutty-hairy-black holes exist in a specific domain of the NUT charge and Gauss-Bonnet parameter. A special emphasis is set on the way the NUT charge affects the solution in the interior of the black hole. Also, we study the influence on the light-like geodesic of both the presence of the scalar field and of the NUT charge. It is found in particular that, mimicking a rotation, the NUT charge leads to a non-planar drift of the trajectories.The paper is organized as follows. In Sect. 2 we present the model, the ansatz for the metric, the boundary conditions of the ensuing classical equations and sketch the form of a perturbative solution. The non-perturbative solutions, obtained with a numerical method, are reported in Sect. 3. The influence of the Gauss-Bonnet gravity term and of the NUT parameter on the light-like geodesics are emphasized in Sect. 4 and illustrated by some figures. Conclusion and perspectives are given in Sect. 5.
The spinning-hairy black holes that occur in Einstein gravity supplemented by a doublet of complex scalar fields are constructed within an extension of the model by a U (1) gauge symmetry involving a massless vector potential. The hairy black holes then acquire an electric charge and a magnetic moment; their domain of existence is discussed in terms of the gauge coupling constant.
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