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.
Newton (Isaac), The Mathematical Principles of Natural Philosophy / traduit et annoté par C. R. Leedham-Green. – Cambridge : Cambridge University Press, 2021. – xlvi + 743 p. – 1 vol. relié de 21 × 26 cm. – isbn 978-1-107-02065-8.
Carnap (Rudolph), Les fondements philosophiques de la physique : une introduction à la philosophie des sciences / traduit par Jean-Mathieu Luccioni et Antonia Soulez ; avant-propos d’Antonia Soulez. – Paris : Librairie philosophique J. Vrin, 2020. – 333 p. – (Mathesis). – 1 vol. broché de 13,5 × 21 cm. – 34,00 €. – isbn 978-2-7116-2876-6.
Le Système de Logique (1843) de John Stuart Mill est souvent considéré comme une œuvre défendant une épistémologie inductiviste. Dans cet article, je me propose de questionner ce statut en me penchant sur la définition de l’induction qui est proposée dans l’ouvrage. Je montre que l’inductivisme de Mill induit une méthodologie de la recherche scientifique dans laquelle les raisonnements déductifs sont aussi, sinon plus, importants que les méthodes inductives, de sorte que l’opposition entre induction et déduction se transforme en complémentarité. Je montre ensuite comment les concepts de loi naturelle et de causalité émergent de ces discussions et j’examine dans quelle mesure les méthodes proposées par Mill peuvent rendre compte des découvertes scientifiques ultérieures.
Wray (K. Brad), Resisting Scientific Realism. – Cambridge : Cambridge University Press, 2018. – 224 p. – 1 vol. broché de 15,5 × 23,5 cm. – £ 49,26. – isbn 978-1-108-41521-7.
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