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ORIGINAL ARTICLE

Cylindrically symmetric fluid in unimodular f (R) gravity ˜ 1,2 Hüseyin Aydın1 · Melis Ulu Dogru

Received: 21 August 2019 / Accepted: 13 November 2019 © Springer Nature B.V. 2019

Abstract In this paper, we examine static cylindrical symmetric fluid in unimodular f (R) gravity. Unimodularity for cylindrical symmetric spacetime geometry is ensured with a coordinate transformation by using tetrad formalism. Field equation solutions for given matter and the spacetime are obtained. Resource of cosmic matter is discussed by using Equation of State (EoS) and energy conditions. We investigate weak and strong energy conditions in unimodular f (R) gravity context with the help of Raychaudhuri equations. Obtained results show that fluids which violate the energy conditions cause the proposed unimodular and cylindrical symmetric wormholes, but this kind of wormholes do not satisfy traversability conditions. Furthermore, the obtained solutions indicate that ω coefficient in EoS must have the condition ω = −1 for physically meaningful fluids. It is discussed whether the result is compatible with the unimodular gravitation theories. Keywords Unimodular f (R) gravity · Energy conditions · Perfect fluid · Cosmological constant · Dark energy · Cylindrical symmetric spacetime · Wormhole

1 Introduction Modern gravity theories intend to find exact explanation of the Universe’s early time inflationary epoch, late time ac-

B M. Ulu Do˜gru

[email protected] H. Aydın [email protected]

1

Department of Physics, Art and Science Faculty, Çanakkale Onsekiz Mart University, 17020, Çanakkale, Turkey

2

Astrophysics Research Center, Çanakkale Onsekiz Mart University, 17020, Çanakkale, Turkey

celeration and transition between the two epochs. Proposals to explain of the cosmic acceleration mostly categorized as modified gravities, dark energy fluids and cosmological constant (Λ) term (Faraoni 2008). f (R) gravity is a modification of general relativity (GR). Buchdahl (1970) proposed the f (R) gravity with a nonlinear Lagrangian. f (R) represents the function of curvature scalar (Buchdahl 1970). f (R) gravity field equations contain higher order derivatives, so it is possible to get more exact solution than GR (Sharif and Arif 2012). f (R) gravity provides various models to investigate of the Universe’s early and late time epochs (De Felice and Tsujikawa 2010). Another of the ways aiming to produce solutions for cosmological constant problem is consideration of classical and/or modified unimodular gravities. In this context, Eichhorn (2015) introduced field equations of unimodular f (R) gravity. Also, Nojiri et al. (2016) described unimodular formalism of f (R) gravity by introducing unimodular Einstein-Hilbert action with Lagrange multiplier in Jordan reference frame. Unimodularity requires that determinant of spacetime metric (g) must be fixed (Anderson and Finkelstein 1971). The determi√ nant satisfies −g =  condition, where  is an arbitrary constant (Eichhorn 2015). In unimodular f (R) gravity, g √ mostly obeys