Thin-shell wormholes in f ( R )-gravity coupled with nonlinear electrodynamics
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Thin-shell wormholes in f (R)-gravity coupled with nonlinear electrodynamics S. Habib Mazharimousavia
, Mustafa Halilsoyb , Khashayar Kianfarc
Department of Physics, Faculty of Arts and Sciences, Eastern Mediterranean University, North Cyprus via Mersin 10, Famagusta, Turkey Received: 8 October 2019 / Accepted: 12 May 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We study the possibility of constructing thin-shell wormhole (TSW) in a particular f (R)-gravity model with nonconstant Ricci scalar and coupled minimally with nonlinear electromagnetic fields. In doing so, first we give a new static spherically symmetric solution of the theory. Then we apply the cut-and-paste method to construct the TSW. As f (R) = 0 we use the specific junction conditions to match the two spacetimes. We find the exact equilibrium radius of the shell from non-black hole solution and show that a linear perturbation leaves the TSW stable.
1 Introduction In Einstein’s general theory of relativity described by the Einstein–Hilbert (EH) action supplemented by an energy-momentum, which is in general exotic, construction of thin-shell wormholes (TSWs) has turned almost into a routine process [1–3]. The original idea by Visser [1–3] was to localize the nonphysical source on a thin-layer, leaving the rest of the bulk with a physical source. Similar constructions of TSWs in modified, highly nonlinear theories have also been attempted [4–7]. Among those modified theories f (R) theory [8–10] has already been much popular during recent decades. In this approach, the action of EH is modified into an arbitrary function of the Ricci scalar R denoted by f (R) -theory. In general, such a theory may attain the EH limit or not. For physical requirements, however, the f (R) theory must reproduce all the experimental tests that Einstein’s theory has successfully passed. Besides, the stability criterion, as well as the absence of ghosts conditions, must be satisfied before the f (R)-theory is considered feasible [11,12]. In this paper our aim is restricted by construction √ of TSWs in a particular f (R)-theory given by f (R) = R + 2α R + R0 + R1 [13,14], in which α, R0 and R1 are dimensionful constant parameters of the theory. For α = 0, the theory reduces to the EH form in which R1 acts as a cosmological constant. Our choice of f (R) relies on an exact solution in the presence of nonlinear electromagnetism. The extended source of our f (R) is provided by a Lagrangian of nonlinear electrodynamics (NED) of the √ 1 form L = − 4π F + 2β −F , in which F = 41 Fμν F μν is the electromagnetic invariant
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] c e-mail: [email protected]
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and β is a constant parameter. In this approach, our NED is powered by a pure electric field without a magnetic component so that from the outset, our problem is assumed static. On
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