Thin shells in F ( R ) gravity with non-constant scalar curvature
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Thin shells in F(R) gravity with non-constant scalar curvature Ernesto F. Eiroaa , Griselda Figueroa Aguirreb Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina Received: 29 May 2020 / Accepted: 19 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We introduce two classes of spherically symmetric spacetimes having a thin shell of matter, in non-quadratic F(R) theories of gravity with non-constant scalar curvature R. In the first, the thin shell joins an inner region with an outer one, while in the second it corresponds to the throat of a wormhole. In both scenarios, we analyze the stability of the static configurations under radial perturbations. As particular examples of spacetimes with a cosmological constant, we present charged thin shells surrounding a non-charged black hole and charged thin-shell wormholes. We show that in both cases stable solutions are possible for suitable values of the parameters.
1 Introduction The difficulties of general relativity in providing a fully accepted explanation to some problems, such as singularities, the nature of the dark matter, the understanding of the accelerated expansion of the Universe, or the case of quantum gravity, motivate the study of modified gravity theories. The simplest proposal is the so-called F(R) theories [1–4], which generalize the Einstein–Hilbert action by replacing the Ricci scalar curvature R with a function of it. They have also an equivalence with the scalar–tensor gravity. These theories offer important applications such as the Starobinsky model which explains the early inflation era of the Universe, and they can give a possible explanation of the acceleration of the Universe expansion without using dark energy. They also provide interesting models for topics such as the cosmic microwave background, weak lensing, structure formation, and the spectra of galaxy clustering, among others. There exist many static spherically symmetric solutions of the field equations in F(R) gravity that can be gathered into two groups: one with constant scalar curvature and the other with non-constant scalar curvature. The first group contains solutions that describe branes [5–7], traversable wormholes [8–13], and black holes [1,3,4,14–22]. The second one consists mostly of black hole solutions [23–27]. Neutron stars [28] and domain wall solutions [29] are also topics of interest addressed in the literature. The conditions for the proper construction of thin shells of matter by cutting and pasting two solutions in general relativity is provided by the well-known Darmois–Israel formalism
a e-mail: [email protected] (corresponding author) b e-mail: [email protected]
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[30–32]. It allows to analyze the characteristics and the dynamics of a thin layer of matter at the matching hypersurface. Due to its simplicity and its malleability, this to
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